Ricci solitons in manifolds with quasi-constant curvature

Abstract

The Eisenhart problem of finding parallel tensors treated already in the framework of quasi-constant curvature manifolds in [15] 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.2000 Math. Subject Classification: 53Cxx; 53C44; 53C21; 53C20; 53C25.

On gradient η-Einstein solitons

“…An important geometrical object in studying Ricci solitons is a symmetric (0, 2)tensor field which is parallel with respect to the Levi-Civita connection [2], [7]. The existence of such tensors on smooth manifolds carrying different structures such as contact [14], K-contact [15], P -Sasakian [11], α-Sasakian [8] etc.…”

Generalized Sasakian-space-forms and Ricci almost solitons with a conformal killing vector field

“…Thereafter Ricci solitons in contact metric manifolds have been studied by various authors such as Bagewadi et. al ( [5], [6], [7], [26]), Bejan and Crasmareanu [8], Blaga [10], Chandra et. al [13], Chen and Deshmukh [14], Deshmukh et.…”

η-Ricci Solitons on Quasi-Sasakian Manifolds

“…An important geometrical object in studying Ricci solitons is well-known to be a symmetric (0, 2)-tensor field which is parallel with respect to the Levi-Civita connection, some of its geometric properties being described in ( [1], [10]) etc. In [3], the author studied the second order parallel tensor field in the context of para-Kenmotsu manifolds admitting η-Ricci solitons.…”