Article · Siberian Advances in Mathematics · January 1, 2011

On conformal Killing symmetric tensor fields on Riemannian manifolds

N. S. Dairbekov, V. A. Sharafutdinov

Abstract

A vector field on Riemannian manifold is called conformal Killing if it generates oneparameter group of conformal transformation. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of the class of conformal Killing vector fields, and appears in different geometric and physical problems. In this paper, we prove that a trace-free conformal Killing tensor field is identically zero if it vanishes on some hypersurface. This statement is a basis of the theorem on decomposition of a symmetric tensor field on a compact manifold with boundary to a sum of three fields of special types. We also establish triviality of the space of trace-free conformal Killing tensor fields on some closed manifolds.

Advanced Differential Geometry ResearchGeometric Analysis and Curvature FlowsRelativity and Gravitational Theoryconformal Killing vectorsRiemannian manifoldshypersurfaces

On conformal Killing symmetric tensor fields on Riemannian manifolds

Abstract

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