Killing vector field Totally Explained

Everything about Killing Vector totally explained

In mathematics, a Killing vector 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. If the metric coefficients

g__X g = lambda g

for some scalar

lambda

. The derivatives of one parameter families of conformal maps are conformal Killing fields. Another generalization is to conformal Killing tensor fields. These are symmetric tensor fields T such that the symmetrization of

abla T

vanishes.

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