nLab
Killing vector

Context

Riemannian geometry

Differential geometry

differential geometry

synthetic differential geometry

Axiomatics

Models

Concepts

Theorems

Applications

Contents

Idea

A Killing vector on a (pseudo-)Riemannian manifold is a covariantly constant vector : a vector field vΓ(TC)v \in \Gamma(T C) that is annihilated by (the symmetrization of) the covariant derivative of the corresponding Levi-Civita connection.

The flows of Killing vectors are isometries of the Riemannian manifold onto itself.

Similarly a Killing spinor is a covariantly constant spinor.

Revised on September 17, 2011 10:48:39 by Urs Schreiber (89.204.137.81)