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:
“Does he who loves someone on account of beauty really love that person? No, for smallpox, which will kill beauty without killing the person, will cause him to love the person no more. And if one loves me for my judgment, for my memory, he does not love me, for I can lose these qualities without losing myself. Where, then, is this myself, if it be neither in the body nor in the soul?”
—Blaise Pascal (1623–1662)
“Hardly a book of human worth, be it heaven’s own secret, is honestly placed before the reader; it is either shunned, given a Periclean funeral oration in a hundred and fifty words, or interred in the potter’s field of the newspapers’ back pages.”
—Edward Dahlberg (1900–1977)