Killing vector

A *Killing vector* on a (pseudo-)Riemannian manifold is a *covariantly constant vector* : a vector field $v \in \Gamma(T C)$ 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)