η-Ricci solitons on N(k)-contact metric manifolds

Abstract

In this paper, we study η-Ricci solitons on N(k)-contact metric manifolds. At first we consider η-Ricci solitons on N(k)-contact metric manifolds with harmonic curvature tensor. Then we study η-Ricci solitons on N(k)-contact metric manifolds with harmonic Weyl tensor. Moreover, we consider η-Ricci soliton on N(k)-contact metric manifolds with η-parallel Ricci tensor. Also η-Ricci soliton on N(k)-contact metric manifolds satisfying some curvature restrictions under projective curvature tensor have been considered. Finally, the existence of an η-Ricci soliton on a 3-dimensional N(k)-contact metric manifold is ensured by a proper example. of constant sectional curvature κ. Further analysis has been done for gradient Einstein soliton, in particular. Obtained results are supported by an illustrative example.