In mathematics, a Killing vector field (often just Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric. Killing fields are the infinitesimal generators of isometries; that is, flows generated by Killing fields are continuous isometries of the manifold. More simply, the flow generates a symmetry, in the sense that moving each point on an object the same distance in the direction of the Killing vector field will not distort distances on the object.
Read more about Killing Vector Field: Explanation
Famous quotes containing the words killing and/or field:
“If we became students of Malcolm X, we would not have young black men out there killing each other like they’re killing each other now. Young black men would not be impregnating young black women at the rate going on now. We’d not have the drugs we have now, or the alcoholism.”
—Spike Lee (b. 1956)
“... many American Jews have a morbid tendency to exaggerate their handicaps and difficulties. ... There is no doubt that the Jew ... has to be twice as good as the average non- Jew to succeed in many a field of endeavor. But to dwell upon these injustices to the point of self-pity is to weaken the personality unnecessarily. Every human being has handicaps of one sort or another. The brave individual accepts them and by accepting conquers them.”
—Agnes E. Meyer (1887–1970)