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:
“Mrs. Finney: Can’t we have some peace in this house, even on New Year’s Eve?
Sadie: You got it mixed up with Christmas. New Year’s Eve is when people go back to killing each other.”
—Joseph L. Mankiewicz (1909–1993)
“Mothers seem to be in subtle competition with teachers. There is always an underlying fear that teachers will do a better job than they have done with their child.... But mostly mothers feel that their areas of competence are very much similar to those of the teacher. In fact they feel they know their child better than anyone else and that the teacher doesn’t possess any special field of authority or expertise.”
—Sara Lawrence Lightfoot (20th century)