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Notes on affine Killing and two-Killing vector fields
Mathematica Slovaca, 2022Abstract In this paper, we investigate the geometry of affine Killing and two-Killing vector fields on Riemannian manifolds. More specifically, a new characterization of an Euclidean space via the affine Killing vector fields are given. Some conditions for an affine Killing and two-Killing vector field to be a conformal (homothetic) or ...
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Killing and Affine Killing Vector Fields
1999We start this chapter with upto date information on divergence theorems and integral formulas. In particular, we provide new information on the validity of divergence theorem for semi-Riemannian manifolds with boundary. Then we review on the existence of Killing and affine Killing vectors and their kinematic and dynamic properties.
Krishan L. Duggal, Ramesh Sharma
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KILLING VECTOR FIELDS OF A SPACETIME
SUT Journal of Mathematics, 1999The author studies geodesics of an \(n\)-dimensional spacetime with a specified metric of constant curvature, which can be classified as one of the de Sitter cases for \(n=4\). It is shown that the geodesics of such spacetimes are plane quadratic curves.
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Spectral Properties of Killing Vector Fields of Constant Length and Bounded Killing Vector Fields
2021This paper is a survey of recent results related to spectral properties of Killing vector fields of constant length and of some their natural generalizations on Riemannian manifolds. One of the main result is the following: If \(\mathfrak {g}\) is a Lie algebra of Killing vector fields on a given Riemannian manifold (M, g), and \(X\in \mathfrak {g ...
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Lorentzian manifolds admitting a killing vector field
Nonlinear Analysis: Theory, Methods & Applications, 1997The author reviews in depth the geometric consequences of the existence of a (non-trivial) Killing vector field \(K\) on a Lorentzian manifold \((M,g)\). He mainly considers the case in which \(K\) satisfies \(g(K,K)
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On Harmonic and Killing Vector Fields
The Annals of Mathematics, 1952Publisher Summary This chapter discusses a formula that gives immediately the proofs of Bochner Theorems for an orientable space and enables to see clearly, the way the contrast between harmonic and Killing vector fields arises. From this general formula, a theorem can be deduced that states that, in a compact orientable Riemannian space with ...
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Harmonic-Killing vector fields on Kähler manifolds.
Bulletin Romanian Mathematical Society, 2000In a previous paper [Bull. Belg. Math. Soc. - Simon Stevin 9, No. 4, 481--490 (2002; Zbl 1044.53052)], the authors introduced the notion of harmonic-Killing (1-harmonic-Killing) vector field \(X\) on a pseudo-Riemannian manifold \((M,g)\) for which the local 1-parameter group of infinitesimal transformations associated to \(X\) is a group of harmonic ...
Dodson, Christopher +2 more
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General relativity from 'localization' of Killing vector fields
Classical and Quantum Gravity, 1993Summary: A new non-standard method of constructing general relativity based on a principal analogical-to-local invariance is suggested. The internal symmetries of an action of any field theory given in a non-dynamic spacetime having Killing vector fields are used as starting point.
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Einstein—Maxwell fields with null Killing vector
Acta Physica Academiae Scientiarum Hungaricae, 1977The field equations for Einstein—Maxwell fields admitting a normal null Killing vector are reduced to a 2-covariant system of equations, which can be derived from a variational principle. Using the invariance of the associated Lagrangian one can generate a class of Einstein—Maxwell fields from the corresponding vacuum solutions.
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