Hadamard manifold

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In mathematics, a Hadamard manifold, named after Jacques Hadamard – sometimes called a Cartan-Hadamard manifold, after Élie Cartan – is a Riemannian manifold (M, g) that is complete and simply-connected, and has everywhere non-positive sectional curvature.

[edit] Examples

• The real line R with its usual metric is a Hadamard manifold with constant sectional curvature equal to 0.
• Standard n-dimensional hyperbolic space Hⁿ is a Hadamard manifold with constant sectional curvature equal to −1.

[edit] See also

• Cartan–Hadamard theorem
• Hadamard space

[edit] References

• Mourougane, Christophe (7 Mar 2001). "Interpolation in non-positively curved Kähler manifolds". Arxiv.org.