Warped geometry

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In physics, warped geometry is a Lorentzian manifold whose metric tensor can be written in form

Note that the geometry almost decomposes into a Cartesian product of the "y" geometry and the "x" geometry - except that the "x"-part is warped, i.e. it is rescaled by a scalar function of the other coordinates "y". For this reason, the metric of a warped geometry is often called a warped product metric.

Warped geometries are the key building block of Randall-Sundrum models in particle physics.

Warped geometries are useful in that separation of variables can be used when solving partial differential equations over them.