synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
A Killing vector on a (pseudo-)Riemannian manifold is equivalently
a covariantly constant vector field : a vector field that is annihilated by (the symmetrization of) the covariant derivative of the corresponding Levi-Civita connection;
Similarly a Killing spinor is a covariantly constant spinor.
For a Riemannian manifold (or pseudo-Riemannian manifold) a vector field is called a Killing vector field if it generates isometries of the metric . More precisely, if, equivalently
the Lie derivative of along vanishes: ;
the flow is a flow by isometries.
The flows of Killing vectors are isometries of the Riemannian manifold onto itself.
Last revised on February 19, 2015 at 15:37:31. See the history of this page for a list of all contributions to it.