Warped geometry

In mathematics and physics, in particular differential geometry and general relativity, a warped geometry is a Riemannian or Lorentzian manifold whose metric tensor can be written in formWarped geometries acquire their full meaning when we substitute the variable y for t, time and x, for s, space. Then the d(y) factor of the spatial dimension becomes the effect of time that in words of Einstein 'curves space'. How it curves space will define one or other solution to a space–time world. For that reason different models of space–time use warped geometries.Many basic solutions of the Einstein field equations are warped geometries, for example, the Schwarzschild solution and the Friedmann–Lemaitre–Robertson–Walker models.3. Chen, Bang-Yen (2017). Differential geometry of warped product manifolds and submanifolds. World Scientific. ISBN 978-981-3208-92-6.