Wikipedia:WikiProject Mathematics/PlanetMath Exchange/53-XX Differential geometry

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This page provides a list of all articles available at PlanetMath in the following topic:

53-XX Differential geometry.

This list will be periodically updated. Each entry in the list has three fields:

1. PM : The first field is the link to the PlanetMath article, along with the article's object ID.
2. WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
3. Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:

Status	means PM article
N	not needed
A	adequately covered
C	copied
M	merged
NC	needs copying
NM	needs merging

• Please update the WP and Status fields as appropriate.
• if the WP field is correct please remove the qualifier "guess".
• If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
• If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
• If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.

Don't forget to include the relevant template if you copy over text or feel like an external link is warranted

• {{planetmath|id=|title=}} for copied over text
• {{planetmath reference|id=|title=}} for an external link

See the main page for examples and usage criteria.

One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.

[edit] 53-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

• PM: closed differential forms on a simply connected domain, id=4146 -- WP guess: closed differential forms on a simply connected domain -- Status:

• PM: distribution, id=6541 -- WP guess: distribution (differential geometry) -- Status: C

Jtwdog 21:16, 21 October 2005 (UTC)

Filled it in ...briefly Robbjedi 03:19, 23 October 2005 (UTC)

• PM: exact (differential form), id=3669 -- WP: exact (differential form) -- Status: A

Jtwdog 21:16, 21 October 2005 (UTC)

• PM: fundamental concepts in differential geometry, id=6441 -- WP guess: fundamental concepts in differential geometry -- Status:

• PM: integral curve, id=5512 -- WP: integral curve -- Status: A

Jtwdog 21:16, 21 October 2005 (UTC)

• PM: Lie bracket, id=5591 -- WP: Lie derivative -- Status: A

linas 04:40, 11 Apr 2005 (UTC)

• PM: Lie derivative, id=3707 -- WP: Lie derivative -- Status: A

linas 04:38, 11 Apr 2005 (UTC)

• PM: Lie derivative (for vector fields), id=5590 -- WP: Lie derivative -- Status: A

linas 04:38, 11 Apr 2005 (UTC)

• PM: locally Euclidean, id=5692 -- WP: locally Euclidean -- Status: A

Jtwdog 21:16, 21 October 2005 (UTC)

• PM: manifold, id=1981 -- WP: manifold -- Status: A

Jtwdog 21:16, 21 October 2005 (UTC)

• PM: manifold, id=5611 -- WP: manifold -- Status: A

Jtwdog 21:16, 21 October 2005 (UTC)

• PM: metric tensor, id=4364 -- WP: metric tensor -- Status: A

linas 04:43, 11 Apr 2005 (UTC)

• PM: notes on the classical definition of a manifold, id=5691 -- WP guess: notes on the classical definition of a manifold -- Status:

• PM: Poincaré lemma, id=5509 -- WP: Poincaré lemma -- Status: NM

linas 19:41, 5 March 2006 (UTC)

• PM: proof of closed differential forms on a simple connected domain, id=4147 -- WP guess: proof of closed differential forms on a simple connected domain -- Status:

• PM: proof of Poincaré lemma, id=5912 -- WP guess: proof of Poincaré lemma -- Status:

• PM: pullback of a k-form, id=4895 -- WP guess: pullback of a k-form -- Status:

• PM: tangent map, id=5506 -- WP guess: tangent map -- Status:

• PM: tangent space, id=2007 -- WP guess: tangent space -- Status: A

Jtwdog 21:16, 21 October 2005 (UTC)

• PM: topological manifold, id=5693 -- WP: topological manifold -- Status: A

linas 04:45, 11 Apr 2005 (UTC)

• PM: bibliography for differential geometry, id=5731 -- WP guess: bibliography for differential geometry -- Status:

• PM: commuting vector fields, id=7205 -- WP guess: commuting vector fields -- Status:

• PM: exhaustion by compact sets, id=7103 -- WP guess: exhaustion by compact sets -- Status:

• PM: integral curve, id=7063 -- WP guess: integral curve -- Status:

• PM: proof of d\alpha (X,Y) = X(\alpha(Y)) - Y(\alpha(X)) - \alpha([X,Y) (global coordinate-free)], id=7472 -- WP: Lie derivative -- Status: N

PM article is confusingly written. linas 19:46, 5 March 2006 (UTC)

• PM: proof of d\alpha (X,Y) = X(\alpha(Y)) - Y(\alpha(X)) - \alpha([X,Y) (local coordinates)], id=7471 -- WP: Lie derivative -- Status: N

PM article is confusingly written. linas 19:46, 5 March 2006 (UTC)

• PM: submersion, id=7335 -- WP: submersion -- Status: A

linas 19:51, 5 March 2006 (UTC)

• PM: proof of exhaustion by compact sets for \mathbb{R}^n, id=7850^new! -- WP guess: proof of exhaustion by compact sets for \mathbbR^n -- Status:

• PM: topological manifold, id=8081^new! -- WP guess: topological manifold -- Status:

[edit] 53-01 Instructional exposition (textbooks, tutorial papers, etc.)

• PM: curl, id=3110 -- WP: curl -- Status: A

Jtwdog 21:19, 21 October 2005 (UTC)

• PM: alternate characterization of curl, id=7341 -- WP guess: alternate characterization of curl -- Status:

• PM: Christoffel symbols, id=7681^new! -- WP guess: Christoffel symbols -- Status:

[edit] 53-03 Historical (must also be assigned at least one classification number from Section 01)

[edit] 53A04 Curves in Euclidean space

• PM: curvature (space curve), id=1632 -- WP guess: curvature (space curve) -- Status:

• PM: Frenet frame, id=1660 -- WP guess: Frenet frame -- Status:

• PM: fundamental theorem of space curves, id=3929 -- WP guess: fundamental theorem of space curves -- Status:

• PM: helix, id=3928 -- WP guess: helix -- Status:

• PM: Serret-Frenet equations, id=1636 -- WP guess: Serret-Frenet equations -- Status:

• PM: space curve, id=1633 -- WP guess: space curve -- Status:

• PM: Classical differential geometry, id=7074 -- WP guess: Classical differential geometry -- Status:

• PM: curvature (plane curve), id=7393 -- WP guess: curvature (plane curve) -- Status:

• PM: cycloid, id=7100 -- WP guess: cycloid -- Status:

• PM: DNA Inequality, id=7390 -- WP guess: DNA Inequality -- Status:

• PM: ellipse, id=7102 -- WP guess: ellipse -- Status:

• PM: example of curvature (space curve), id=7624 -- WP guess: example of curvature (space curve) -- Status:

• PM: expressions for curvature and torsion, id=7567 -- WP guess: expressions for curvature and torsion -- Status:

• PM: famous curves, id=7073 -- WP guess: famous curves -- Status:

• PM: line in the plane, id=7108 -- WP guess: line in the plane -- Status:

• PM: Mean Curvature, id=7392 -- WP guess: Mean Curvature -- Status:

• PM: Serret-Frenet equations in \mathbb{R}^2, id=7072 -- WP guess: Serret-Frenet equations in \mathbbR^2 -- Status:

• PM: sinusoid, id=7101 -- WP guess: sinusoid -- Status:

• PM: circle of curvature, id=9277^new! -- WP guess: circle of curvature -- Status:

• PM: curvature determines the curve, id=9353^new! -- WP guess: curvature determines the curve -- Status:

• PM: curvature of a circle, id=7820^new! -- WP guess: curvature of a circle -- Status:

• PM: curvature of Nielsen's spiral, id=9350^new! -- WP guess: curvature of Nielsen's spiral -- Status:

• PM: easy calculation of the area of an ellipse, id=7689^new! -- WP guess: easy calculation of the area of an ellipse -- Status:

• PM: moving frame, id=8606^new! -- WP guess: moving frame -- Status:

• PM: order of contact, id=9278^new! -- WP guess: order of contact -- Status:

[edit] 53A05 Surfaces in Euclidean space

• PM: Pappus's centroid theorem, id=7321 -- WP guess: Pappus's centroid theorem -- Status:

• PM: second fundamental form, id=7339 -- WP: second fundamental form -- Status: NM

linas 19:55, 5 March 2006 (UTC)

• PM: Gauss-Bonnet theorem, id=8807^new! -- WP guess: Gauss-Bonnet theorem -- Status:

• PM: Gauss-Bonnet theorem, id=8824^new! -- WP guess: Gauss-Bonnet theorem -- Status:

• PM: Gaussian curvature, id=9299^new! -- WP guess: Gaussian curvature -- Status:

• PM: shape operator, id=8132^new! -- WP guess: shape operator -- Status:

[edit] 53A17 Kinematics

[edit] 53A30 Conformal differential geometry

[edit] 53A35 Non-Euclidean differential geometry

• PM: Smarandache geometries, id=5769 -- WP: Smarandache geometries -- Status: N

PM article is "not found", this PM link is broken? linas 19:37, 5 March 2006 (UTC)

• PM: Smarandache geometries, id=7327 -- WP: Smarandache geometries -- Status: NC

Current WP link is redirect to biography of Smarandache. 19:37, 5 March 2006 (UTC)

[edit] 53A45 Vector and tensor analysis

• PM: closed (differential form), id=3668 -- WP: closed (differential form) -- Status: A

Jtwdog 21:21, 21 October 2005 (UTC)

• PM: axial vector, id=7031 -- WP: axial vector -- Status: A

linas 19:09, 5 March 2006 (UTC)

• PM: circulation and vorticity, id=9611^new! -- WP guess: circulation and vorticity -- Status:

• PM: continuity equation, id=7944^new! -- WP guess: continuity equation -- Status:

• PM: derivation of the Laplacian from rectangular to spherical coordinates, id=9376^new! -- WP guess: derivation of the Laplacian from rectangular to spherical coordinates -- Status:

• PM: derivation of unit vectors in curvilinear coordinates, id=9321^new! -- WP guess: derivation of unit vectors in curvilinear coordinates -- Status:

• PM: motion of continuum, id=7889^new! -- WP guess: motion of continuum -- Status:

• PM: Reynolds transport theorem, id=8048^new! -- WP guess: Reynolds transport theorem -- Status:

• PM: time dilatation of a volume element, id=7911^new! -- WP guess: time dilatation of a volume element -- Status:

• PM: topics on vectors, id=7804^new! -- WP guess: topics on vectors -- Status:

• PM: vector fields: Lagrangian and Eulerian description, id=7863^new! -- WP guess: vector fields: Lagrangian and Eulerian description -- Status:

[edit] 53A55 Differential invariants (local theory), geometric objects

• PM: Riemann curvature tensor, id=8592^new! -- WP guess: Riemann curvature tensor -- Status:

[edit] 53A99 Miscellaneous

• PM: Euclidean distance, id=1318 -- WP guess: Euclidean distance -- Status:

• PM: some structures on \mathbb{R}^n, id=5419 -- WP guess: some structures on \mathbbR^n -- Status:

[edit] 53Axx Classical differential geometry

[edit] 53B05 Linear and affine connections

• PM: affine connection, id=6191 -- WP: affine connection -- Status: NM

linas 04:23, 11 Apr 2005 (UTC)

• PM: conjugate points, id=6159 -- WP guess: conjugate points -- Status:

• PM: connection, id=2880 -- WP: connection -- Status: NM

The PM article is quite a bit larger linas 04:25, 11 Apr 2005 (UTC)

• PM: Levi-Civita connection, id=4765 -- WP: Levi-Civita connection -- Status: A

linas 04:29, 11 Apr 2005 (UTC)

• PM: Riemann normal coordinates, id=6157 -- WP guess: Riemann normal coordinates -- Status:

• PM: vector field along a curve, id=4755 -- WP guess: vector field along a curve -- Status:

[edit] 53B20 Local Riemannian geometry

• PM: Euclidean space as a manifold, id=7355 -- WP guess: Euclidean space as a manifold -- Status:

• PM: first fundamental form, id=7332 -- WP guess: first fundamental form -- Status:

• PM: first order operators in Riemannian geometry, id=7325 -- WP guess: first order operators in Riemannian geometry -- Status:

• PM: formulas in Riemannian geometry, id=7446 -- WP guess: formulas in Riemannian geometry -- Status:

• PM: sectional curvature, id=7907^new! -- WP guess: sectional curvature -- Status:

• PM: sectional curvature determines Riemann curvature tensor, id=7924^new! -- WP guess: sectional curvature determines Riemann curvature tensor -- Status:

[edit] 53B21 Methods of Riemannian geometry

• PM: Hodge star operator, id=4120 -- WP: Hodge star operator -- Status: NM

• PM: Riemannian manifold, id=3452 -- WP: Riemannian manifold -- Status: NM

[edit] 53B25 Local submanifolds

[edit] 53B99 Miscellaneous

• PM: example of rewriting a differential equation as a Pfaffian system, id=6235 -- WP guess: example of rewriting a differential equation as a Pfaffian system -- Status:

• PM: germ of smooth functions, id=3501 -- WP guess: germ of smooth functions -- Status:

• PM: Pfaff's problem, id=6210 -- WP guess: Pfaff's problem -- Status:

• PM: germ, id=9801^new! -- WP guess: germ -- Status:

[edit] 53Bxx Local differential geometry

[edit] 53C17 Sub-Riemannian geometry

• PM: Sub-Riemannian manifold, id=4754 -- WP: Sub-Riemannian manifold -- Status: A

linas 04:48, 11 Apr 2005 (UTC)

[edit] 53C20 Global Riemannian geometry, including pinching

• PM: sphere theorem from global differential geometry, id=7905^new! -- WP guess: sphere theorem from global differential geometry -- Status:

[edit] 53C21 Methods of Riemannian geometry, including PDE methods; curvature restrictions

[edit] 53C22 Geodesics

• PM: affine parameter, id=6164 -- WP guess: affine parameter -- Status:

• PM: geodesic, id=5513 -- WP: geodesic -- Status: A

linas 04:33, 11 Apr 2005 (UTC)

• PM: geodesic triangle, id=9510^new! -- WP guess: geodesic triangle -- Status:

[edit] 53C26 Hyper-Kähler and quaternionic Kähler geometry, ``special geometry

• PM: hyperkähler manifold, id=7813^new! -- WP guess: hyperkähler manifold -- Status:

[edit] 53C40 Global submanifolds

[edit] 53C42 Immersions (minimal, prescribed curvature, tight, etc.)

• PM: Nash isometric embedding theorem, id=7569 -- WP: Nash isometric embedding theorem -- Status: NC

linas 20:06, 5 March 2006 (UTC)

[edit] 53C60 Finsler spaces and generalizations (areal metrics)

• PM: spray space, id=7372 -- WP: spray space -- Status: NC

linas 20:05, 5 March 2006 (UTC)

[edit] 53Cxx Global differential geometry

[edit] 53D05 Symplectic manifolds, general

• PM: almost complex structure, id=3739 -- WP: almost complex structure -- Status: A

linas 17:45, 5 March 2006 (UTC)

• PM: coadjoint orbit, id=4760 -- WP: coadjoint orbit -- Status: NM

linas 17:49, 5 March 2006 (UTC)

• PM: Darboux's Theorem (symplectic geometry), id=3738 -- WP: Darboux's theorem -- Status: A

linas 18:15, 5 March 2006 (UTC)

• PM: examples of symplectic manifolds, id=3672 -- WP: symplectic manifold -- Status: NM

linas 18:19, 5 March 2006 (UTC)

• PM: Hamilton equations, id=6410 -- WP: Hamilton's equations -- Status: NM

linas 18:29, 5 March 2006 (UTC)

• PM: Hamiltonian vector field, id=3706 -- WP: Hamiltonian vector field -- Status: A

Jtwdog 21:37, 21 October 2005 (UTC)

• PM: if the algebra of functions on a manifold is a Poisson ring then the manifold is symplectic, id=6422 -- WP: Poisson ring -- Status: N

Its a proof, can be replaced by a sentance and a ref in WP. linas 17:09, 5 March 2006 (UTC)

• PM: isotropic submanifold, id=3670 -- WP: isotropic submanifold -- Status: NC

current WP article is a redirect. linas 18:33, 5 March 2006 (UTC)

• PM: lagrangian submanifold, id=3671 -- WP: lagrangian submanifold -- Status: A

PM article is a stub, WP article is redirect.linas 18:36, 5 March 2006 (UTC)

• PM: Moser's theorem, id=3806 -- WP: Moser's theorem -- Status: NC

linas 18:38, 5 March 2006 (UTC)

• PM: Poisson bracket, id=6412 -- WP: Poisson bracket -- Status: A

linas 20:03, 5 March 2006 (UTC)

• PM: Poisson ring, id=6414 -- WP: Poisson ring -- Status: C

linas 04:54, 11 Apr 2005 (UTC)

linas 17:06, 5 March 2006 (UTC)

• PM: proof of Darboux's Theorem (symplectic geometry), id=5589 -- WP: Darboux's Theorem -- Status: N

added ref to WP article. linas 21:07, 5 March 2006 (UTC)

• PM: symplectic manifold, id=3667 -- WP: symplectic manifold -- Status: NM

This should be a trival merge, just pick up def for symplectomorphism, and defn of non-degeneracy. linas 04:53, 11 Apr 2005 (UTC)

• PM: symplectic matrix, id=4140 -- WP: symplectic matrix -- Status: A

linas 04:53, 11 Apr 2005 (UTC)

• PM: symplectic vector field, id=3705 -- WP: symplectic vector field -- Status: M

linas 18:53, 5 March 2006 (UTC)

• PM: symplectic vector space, id=4138 -- WP: symplectic vector space -- Status: A

linas 18:55, 5 March 2006 (UTC)

• PM: Examples of lagrangian submanifolds, id=7099 -- WP: Lagrangian submanifold -- Status: NM

linas 19:07, 5 March 2006 (UTC)

• PM: The characteristic polynomial of a symplectic matrix is a reciprocal polynomial, id=7455 -- WP: Symplectic matrix -- Status: NM

Actually, symplectic matrix article just needs a statement of the theorem. linas 19:05, 5 March 2006 (UTC)

• PM: concepts in symplectic geometry, id=6423^new! -- WP guess: concepts in symplectic geometry -- Status:

• PM: every symplectic manifold has even dimension, id=7685^new! -- WP guess: every symplectic manifold has even dimension -- Status:

[edit] 53D10 Contact manifolds, general

• PM: contact manifold, id=4409 -- WP: contact manifold -- Status: NM

linas 19:29, 5 March 2006 (UTC)

[edit] 53D20 Momentum maps; symplectic reduction

• PM: momentum map, id=3718 -- WP: momentum map -- Status: A

linas 19:17, 5 March 2006 (UTC)

[edit] 53D50 Geometric quantization

[edit] 53D99 Miscellaneous

• PM: \mathbb{C} as a Kähler manifold, id=7733^new! -- WP guess: \mathbbC as a Kähler manifold -- Status:

• PM: a Kähler manifold is symplectic, id=8203^new! -- WP guess: a Kähler manifold is symplectic -- Status:

• PM: Kähler manifold, id=7673^new! -- WP guess: Kähler manifold -- Status:

• PM: Kähler potential, id=8740^new! -- WP guess: Kähler potential -- Status:

[edit] 53Dxx Symplectic geometry, contact geometry

[edit] 53Z05 Applications to physics

• PM: Minkowski space, id=8393^new! -- WP guess: Minkowski space -- Status:

• PM: pseudo-Riemannian manifold, id=7688^new! -- WP guess: pseudo-Riemannian manifold -- Status: