Generalized Ricci solitons and Einstein metrics on weak K-contact manifolds

Abstract

We study so-called "weak" metric structures on a smooth manifold, which generalize the metric contact and $ K $-contact structures and allow a new look at the classical theory. We characterize weak $ K $-contact manifolds among all weak contact metric manifolds using the property well known for $ K $-contact manifolds, as well as find when a Riemannian manifold endowed with a unit Killing vector field is a weak $ K $-contact manifold. We also find sufficient conditions for a weak $ K $-contact manifold with a parallel Ricci tensor or with a generalized Ricci soliton structure to be an Einstein manifold.

Keywords

• weak $ k $-contact manifold
• unit killing vector field
• generalized ricci soliton
• einstein metric
• curvature