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Harmonic-Killing vector fields on Kähler manifolds.
Bulletin Romanian Mathematical Society, 2000 In 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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Spectral Properties of Killing Vector Fields of Constant Length and Bounded Killing Vector Fields
Trends in Mathematics, 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 ...
Yury Nikonorov
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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 ...
Wenjie Wang
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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.
Tominosuke Otsuki
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On Discrete Killing Vector Fields and Patterns on Surfaces
Computer Graphics Forum, 2010 AbstractSymmetry is one of the most important properties of a shape, unifying form and function. It encodes semantic information on one hand, and affects the shape's aesthetic value on the other. Symmetry comes in many flavors, amongst the most interesting being intrinsic symmetry, which is defined only in terms of the intrinsic geometry of the shape ...
Ben-Chen, Mirela +3 more
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On the Killing vector fields of generalized metrics
SUT Journal of Mathematics, 2004For a given manifold \(M\) endowed with a metric tensor pulled back to its tangent bundle by its own projection, the author gives necessary and sufficient conditions for a vector field to be an infinitesimal isometry of a metric of this type, in general and for some special classes.
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On the geometry of orbits of killing vector fields
Differential Equations, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Narmanov, A. Ya., Saitova, S. S.
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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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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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The exterior derivative as a Killing vector field
Israel Journal of Mathematics, 1996The authors prove that for any graded metric on a graded manifold there exists a unique torsionless and metric graded connection. The formula used to define the metric graded connection coincides with the one given by the reviewer for even metrics on supermanifolds [cf. the reviewer, Preprint, Seminarul de Mecanica, Univ. Timisoara 30 (1990)]. Starting
Monterde, J., Sánchez-Valenzuela, O. A.
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