On conformal Killing symmetric tensor fields on Riemannian manifolds

By Nurlan S. Dairbekov, Vladimir A. Sharafutdinov. 2011

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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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4cda9272e71f2a06e1a3d2eed7992c28e70a2b9c

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In Applied Mathematics

In Astronomy and Astrophysics

In Mathematical Physics

Citations in the corpus

Invariant distributions, Beurling transforms and tensor tomography in higher dimensions (2014, background): “Section 3 follows [11,23] and discusses spherical harmonic expansions in the vertical variable, which generalize Fourier expansions in the angular variable for dim M = 2.”