Ricci solitons in manifolds with quasi-constant curvature

Details Ricci solitons in manifolds with quasi-constant curvature Ricci solitons in manifolds with quasi-constant curvature

2010-06-24

arxiv.org/abs/1006.4737v1

Mathematics

Differential Geometry

10 pages

Scientific paper

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.

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