Warped geometry

In mathematics and physics, in particular in differential geometry and general relativity, the distorted product of two pseudo - Riemannian manifolds means the product manifold with the warped product metric.

Definition

Under the distorted product of two pseudo - Riemannian manifolds and along a strictly positive function is defined as the product manifold equipped with the metric tensor. This call and the natural submersions and the pullback of a tensor under a mapping g between two manifolds. This is called the base and as a fiber of the product manifold.

Definition of distorted metrics

Under a distorted product metric is defined as a Riemannian or Lorentzian manifold whose metric by

Can be displayed. That is especially decomposes the observed diversity in the Cartesian product of a "y" - and an "x " geometry, where the " x" metric is distorted.