Schur-type inequality for solitonic hypersurfaces in $ (k, \mu) $-contact metric manifolds

Abstract

In this article, we derive a Schur-type Inequality in terms of the gradient $ r $-Almost Newton-Ricci-Yamabe soliton in $ (k, \mu) $-contact metric manifolds. We discuss the triviality for the compact gradient $ r $-Almost Newton-Ricci-Yamabe soliton in $ (k, \mu) $-Contact metric manifolds. In the end, we deduce a Schur-type inequality for the gradient $ r $-Almost Newton-Yamabe soliton in $ (k, \mu) $-contact metric manifolds, static Riemannian manifolds, and normal homogeneous compact Riemannian manifolds coupled with a projected Casimir operator.

Keywords

• $ (k, \mu) $-contact metric manifold
• schur-type inequality
• hypersurfaces
• gradient $ r $-almost newton-ricci-yamabe solitons