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...

conformal Killing vector field on a manifold of dimension n with (pseudo) Riemannian metric g {\displaystyle g} (also called a conformal Killing vector, CKV...

Einstein field equations. Mathematically a Killing horizon is a null hypersurface defined by the vanishing of the norm of a Killing vector field (both are...

generalization of a Killing vector field Killing vector field or Killing field, a vector field on a Riemannian manifold The Killing form, a symmetric bilinear...

thus, this Killing vector field is hypersurface orthogonal. The fact that the spacetime admits an irrotational timelike Killing vector field is in fact...

Killing vector field, a vector field on a Riemannian manifold Solenoidal vector field, a vector field with zero divergence Vector potential, a vector...

thus, this Killing vector field is hypersurface orthogonal. The fact that our spacetime admits an irrotational timelike Killing vector field is in fact...

In vector calculus, a complex lamellar vector field is a vector field which is orthogonal to a family of surfaces. In the broader context of differential...

{\mathcal {L}}_{Y}]T.} A Killing vector field is one of the most important types of symmetries and is defined to be a smooth vector field X that preserves the...

mathematics, a Killing tensor or Killing tensor field is a generalization of a Killing vector, for symmetric tensor fields instead of just vector fields. It is...

Look up killing field or Killing Fields in Wiktionary, the free dictionary. Killing field may also refer to: Killing Fields, a number of sites in Cambodia...

A projective vector field (projective) is a smooth vector field on a semi Riemannian manifold (p.ex. spacetime) M {\displaystyle M} whose flow preserves...

spacetime is static if it admits a global, non-vanishing, timelike Killing vector field K {\displaystyle K} which is irrotational, i.e., whose orthogonal...

In Riemannian geometry, a Jacobi field is a vector field along a geodesic γ {\displaystyle \gamma } in a Riemannian manifold describing the difference...

I(\rho )} is the index of the representation. Casimir invariant Killing vector field Kirillov 2008, p. 102. Borel 2001, p. 5 Fulton, William; Harris,...

which is the gravitational force field. Consequently, if ξ μ {\displaystyle \xi ^{\mu }} is any Killing vector field, then the conservation law associated...

on the spacetime metric. In a stationary spacetime with timelike Killing vector field ξ {\displaystyle \xi } , the temperature T {\displaystyle T} satisfies...

kind of spinor field related to Killing vector fields and Killing tensors. If M {\displaystyle {\mathcal {M}}} is a manifold with a Killing spinor, then...

t 0 {\displaystyle t=t_{0}} admit a Bianchi III (c.f. the fourth Killing vector field). This can be rewritten as the symmetry group containing three-dimensional...

{L}}_{X}g_{ab})_{;c}=0} Conformal vector field Curvature collineation Homothetic vector field Killing vector field Matter collineation Spacetime symmetries...

S2CID 121548146. Killing equation Killing form Killing–Hopf theorem Killing horizon Killing spinor Killing tensor Killing vector field Levi decomposition...

relativity, specifically in the Einstein field equations, a spacetime is said to be stationary if it admits a Killing vector that is asymptotically timelike....

change of a tensor field (including scalar functions, vector fields and one-forms), along the flow defined by another vector field. This change is coordinate...

it can be regarded as a constant vector field. In particular, the spin angular velocity is a Killing vector field belonging to an element of the Lie...

by similarity reduction. Affine vector field Conformal Killing vector field Curvature collineation Killing vector field Matter collineation Spacetime symmetries...

spacetime, a spacetime having a global, non-vanishing, timelike Killing vector field which is irrotational Statics, a branch of physics concerned with...

electromagnetic field, a Killing vector field does not necessarily preserve the electric and magnetic fields. Affine vector field Conformal vector field Curvature...

In mathematics, Salomon Bochner proved in 1946 that any Killing vector field of a compact Riemannian manifold with negative Ricci curvature must be zero...

linearly independent Killing vector fields. Indeed, in the Cartesian chart we can readily find ten linearly independent Killing vector fields, generating respectively...

set of ⁠1/2⁠N(N + 1) Killing vectors. For three dimensions, this gives a total of six linearly independent Killing vector fields; homogeneous 3-spaces...