Comparison To Surfaces
This relationship between a local invariant, the curvature, and a global topological invariant, the index, is characteristic of results in higher-dimensional Riemannian geometry such as the Gauss–Bonnet theorem.
Read more about this topic: Total Curvature
Famous quotes containing the words comparison to, comparison and/or surfaces:
“It is very important not to become hard. The artist must always have one skin too few in comparison to other people, so you feel the slightest wind.”
—Shusha Guppy (b. 1938)
“[Girls] study under the paralyzing idea that their acquirements cannot be brought into practical use. They may subserve the purposes of promoting individual domestic pleasure and social enjoyment in conversation, but what are they in comparison with the grand stimulation of independence and self- reliance, of the capability of contributing to the comfort and happiness of those whom they love as their own souls?”
—Sarah M. Grimke (1792–1873)
“But ice-crunching and loud gum-chewing, together with drumming on tables, and whistling the same tune seventy times in succession, because they indicate an indifference on the part of the perpetrator to the rest of the world in general, are not only registered on the delicate surfaces of the brain but eat little holes in it until it finally collapses or blows up.”
—Robert Benchley (1889–1945)