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:
“Books are the best things, well used; abused, among the worst. What is the right use? What is the one end, which all means go to effect? They are for nothing but to inspire. I had better never see a book, than to be warped by its attraction clean out of my own orbit, and made a satellite instead of a system.”
—Ralph Waldo Emerson (1803–1882)
“... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It’s not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I’m able to avoid or manipulate or process pain.”
—Louise Bourgeois (b. 1911)