Parallel tensors and Ricci solitons in \(N(k)\)-quasi Einstein manifolds (Q1758652)

The present paper deals with the well-known Einstein problem of finding parallel and symmetric tensors in the framework of \(N(k)\)-quasi Einstein manifolds. The main result is related to the recent theory of Ricci solitons. The author proves that if the generator of the manifold provides a Ricci soliton then it is: i) shrinking on a class of conformally flat perfect fluid space-time and on quasi-umbilical hypersurfaces, in particular unit spheres; ii) expanding if the generator is of torse-forming type.