Ricci solitons in manifolds with quasi-constant curvature

By Cornelia-Livia Bejan, Mircea Crasmareanu. 2010

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The Eisenhart problem of nding parallel tensors treated already in the framework of quasi-constant curvature manifolds in [Jia] 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 eld and ii) shrinking on a class of orientable quasi-umbilical hypersurfaces of a real projective space=elliptic space form.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b0e7c6c98a567e43270cbcd0cd532d7d20b3db44