Warped geometry
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In physics, warped geometry is a special type of metric in general relativity that can be written in the form
- <math>ds^2 = g_{ab} dy^a dy^b + f(y) g_{ij} dx^i dx^j<math>
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".
Warped geometries are the key building block of Randall-Sundrum models in particle physics.
The really nice thing about warped geometries is that we can perform a separation of variables when solving partial differential equations over it.