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Ricci solitons in manifolds with quasi-constant curvature

Research paper by Cornelia Livia Bejan, Mircea Crasmareanu

Indexed on: 24 Jun '10Published on: 24 Jun '10Published in: Mathematics - Differential Geometry



Abstract

The Eisenhart problem of finding parallel tensors treated already in the framework of quasi-constant curvature manifolds in \cite{x:j} is reconsidered for the symmetric case and the result is interpreted in terms of Ricci solitons. If the generator of the manifold provides a Ricci soliton then this is i) expanding on para-Sasakian spaces with constant scalar curvature and vanishing $D$-concircular tensor field and ii) shrinking on a class of orientable quasi-umbilical hypersurfaces of a real projective space=elliptic space form.