Abstract
<abstract><p>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.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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