Almost $\eta$-Ricci solitons in $(LCS{)}_n$-manifolds

Abstract

We consider almost $\eta$-Ricci solitons in $(LCS{)}_n$-manifolds satisfying certain curvature conditions. We provide a lower and an upper bound for the norm of the Ricci curvature in the gradient case, derive a Bochner-type formula for an almost $\eta$-Ricci soliton and state some consequences of it on an $(LCS{)}_n$-manifold.

15 pages

References in corpus (2)

• $\eta$-Ricci solitons in $(\epsilon )$-almost paracontact metric manifolds
• Ricci solitons on Ricci pseudosymmetric $(LCS{)}_n$-manifolds