Warped product

Warped product ${\displaystyle F\times _{f}B}$ of two Riemannian (or pseudo-Riemannian) manifolds ${\displaystyle F=(F,h)}$ and ${\displaystyle B=(B,g)}$ with respect to a function ${\displaystyle f\colon B\to \mathbb {R} }$ is the product space ${\displaystyle F\times B}$ with the metric tensor ${\displaystyle g\oplus (f^{2}\cdot h)}$.

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