Vector field on a Riemannian manifold that preserves the metric
In mathematics, a Killing vector field (often called a 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 of an object the same distance in the direction of the Killing vector will not distort distances on the object.
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In mathematics, a Killingvectorfield (often called a Killingfield), named after Wilhelm Killing, is a vectorfield on a Riemannian manifold (or pseudo-Riemannian...
conformal Killingvectorfield on a manifold of dimension n with (pseudo) Riemannian metric g {\displaystyle g} (also called a conformal Killingvector, CKV...
Einstein field equations. Mathematically a Killing horizon is a null hypersurface defined by the vanishing of the norm of a Killingvectorfield (both are...
mathematics, a Killing tensor or Killing tensor field is a generalization of a Killingvector, for symmetric tensor fields instead of just vectorfields. It is...
In vector calculus, a complex lamellar vectorfield is a vectorfield which is orthogonal to a family of surfaces. In the broader context of differential...
In Riemannian geometry, a Jacobi field is a vectorfield along a geodesic γ {\displaystyle \gamma } in a Riemannian manifold describing the difference...
{\mathcal {L}}_{Y}]T.} A Killingvectorfield is one of the most important types of symmetries and is defined to be a smooth vectorfield X that preserves the...
spacetime is static if it admits a global, non-vanishing, timelike Killingvectorfield K {\displaystyle K} which is irrotational, i.e., whose orthogonal...
A projective vectorfield (projective) is a smooth vectorfield on a semi Riemannian manifold (p.ex. spacetime) M {\displaystyle M} whose flow preserves...
spacetime can be defined as a spacetime which possesses a timelike Killingvectorfield. The following discussion is an expanded and simplified version of...
relativity, specifically in the Einstein field equations, a spacetime is said to be stationary if it admits a Killingvector that is asymptotically timelike....
kind of spinor field related to Killingvectorfields and Killing tensors. If M {\displaystyle {\mathcal {M}}} is a manifold with a Killing spinor, then...
change of a tensor field (including scalar functions, vectorfields and one-forms), along the flow defined by another vectorfield. This change is coordinate...
spacetime, a spacetime having a global, non-vanishing, timelike Killingvectorfield which is irrotational Statics, a branch of physics concerned with...
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