Parallel tensors and Ricci solitons in N (k)-quasi Einstein manifolds
M Crasmareanu - Indian Journal of Pure and Applied Mathematics, 2012 - Springer
Indian Journal of Pure and Applied Mathematics, 2012•Springer
The Eisenhart problem of finding parallel and symmetric tensors is considered in the
framework of N (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.
framework of N (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.
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.
Springer
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