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 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 useful in that separation of variables can be used when solving partial differential equations over them.
Read more about Warped Geometry: Examples
Famous quotes containing the words warped and/or geometry:
“With respect to a true culture and manhood, we are essentially provincial still, not metropolitan,—mere Jonathans. We are provincial, because we do not find at home our standards; because we do not worship truth, but the reflection of truth; because we are warped and narrowed by an exclusive devotion to trade and commerce and manufacturers and agriculture and the like, which are but means, and not the end.”
—Henry David Thoreau (1817–1862)
“The geometry of landscape and situation seems to create its own systems of time, the sense of a dynamic element which is cinematising the events of the canvas, translating a posture or ceremony into dynamic terms. The greatest movie of the 20th century is the Mona Lisa, just as the greatest novel is Gray’s Anatomy.”
—J.G. (James Graham)