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

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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.

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Authors and Affiliations

  1. Faculty of Mathematics, University “Al. I.Cuza”, Iaşi, 700506, Romania

    Mircea Crasmareanu

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  1. Mircea Crasmareanu
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Crasmareanu, M. Parallel tensors and Ricci solitons in N (k)-quasi Einstein manifolds. Indian J Pure Appl Math 43, 359–369 (2012). https://doi.org/10.1007/s13226-012-0022-3

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  • DOI: https://doi.org/10.1007/s13226-012-0022-3

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