Killing vector

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Killing vector

[¦kil·iŋ ¦vek·tər]
(mathematics)
An element of a vector field in a geometry that generates an isometry.
References in periodicals archive ?
In particular, a conformal vector field with a vanishing conformal coefficient reduces to a Killing vector field.
Clearly, a Ricci soliton with V zero or a Killing vector field reduces to an Einstein metric.
If V is the gradient of a smooth function f, up to the addition of a Killing vector field, then we can replace V by [bar.
Keywords and Phrases: Quasi Einstein manifolds, Super quasi Einstein manifolds, Generalized quasi-Einstein manifolds, Killing vector field, Harmonic vector field, Projective Killing vector field, Conformal Killing vector field, Sectional curvature.
If X is a Killing vector field, then divX = 0, where 'div' denotes divergence.
xi]][xi] = 0 and [xi] is [nabla]-parallel if and only if it is a Killing vector field.
For a stationary space-time metric, there exists a vector field called a time-like Killing vector field.
The null hypersurface of such space-time admits a nonvanishing Killing vector field, say l, which may or may not be the Killing vector field of the landing space-time.
Note that VV is a Killing vector field if and only if the fundamental tensor T vanishes identically, that is, the fibers are totally geodesies.
Moreover, [xi] is a Killing vector field if and only if M is a quasi-Sasakian manifold, that is d[PHI] = 0, where [PHI](X, Y) = g(X, fY).
Lie derivatives are applied to conformal invariance, first integrals, Killing vector fields, and symmetries of differential equations.
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