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Mat. Tr., 2010, Volume 13, Number 1, Pages 85–145 (Mi mt192)  

This article is cited in 13 scientific papers (total in 13 papers)

On conformal Killing symmetric tensor fields on Riemannian manifolds

N. S. Dairbekova, V. A. Sharafutdinovb

a Kazakh-British Technical University, Almaty, Kazakhstan
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

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.

Key words: Riemannian geometry, tensor analysis, conformal Killing tensor field.

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English version:
Siberian Advances in Mathematics, 2011, 21:1, 1–41

Bibliographic databases:

Document Type: Article
UDC: 517.98
Received: 24.08.2009

Citation: N. S. Dairbekov, V. A. Sharafutdinov, “On conformal Killing symmetric tensor fields on Riemannian manifolds”, Mat. Tr., 13:1 (2010), 85–145; Siberian Adv. Math., 21:1 (2011), 1–41

Citation in format AMSBIB
\by N.~S.~Dairbekov, V.~A.~Sharafutdinov
\paper On conformal Killing symmetric tensor fields on Riemannian manifolds
\jour Mat. Tr.
\yr 2010
\vol 13
\issue 1
\pages 85--145
\jour Siberian Adv. Math.
\yr 2011
\vol 21
\issue 1
\pages 1--41

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