Parallel tensors and Ricci solitons in N (k)-quasi Einstein manifolds

Mircea Crasmareanu ()
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Mircea Crasmareanu: University “Al. I.Cuza”

Indian Journal of Pure and Applied Mathematics, 2012, vol. 43, issue 4, 359-369

Abstract: Abstract The Eisenhart problem of finding parallel and symmetric tensors is considered in the framework ofN (k)-quasi Einstein manifolds and the result is connected with Ricci solitons. If the generator of the manifold provides a Ricci soliton then this is: i) shrinking on a class of conformally flat perfect fluid space-times and on quasi-umbilical hypersurfaces, in particular unit spheres; ii) expanding if the generator is of torse-forming type.

Keywords: Parallel second order covariant tensor field; N (k)-quasi Einstein manifold; torse-forming vector field; Ricci soliton; perfect fluid (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s13226-012-0022-3

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