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:
“when Mrs Kindhead comes to collect for the Community Chest
grab her and tell her There are unfavorable omens in the sky!
And when the mayor comes to get my vote tell him
When are you going to stop people killing whales!”
—Gregory Corso (b. 1930)
“In the beginning, I wanted to enter what was essentially a man’s field. I wanted to prove I could do it. Then I found that when I did as well as the men in the field I got more credit for my work because I am a woman, which seems unfair.”
—Eugenie Clark (b. 1922)