On conformal Killing symmetric tensor fields on Riemannian manifolds |
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Authors: | N. S. Dairbekov V. A. Sharafutdinov |
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Affiliation: | (1) Departamento de Matemática, Instituto Superior Técnico, CAMGSD, Av. Rovisco Pais, 1049-001 Lisboa, Portugal |
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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. |
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