2023/01/09 by Vladimir Rovenski, Rovenski, Vladimir
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2301.03500
openalex publication_date 2023/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study metric structures on a smooth manifold (introduced in our recent works and called a weak contact metric structure and a weak K-structure) which generalize the metric contact and K-contact structures, and allow a new look at the classical theory. First, we characterize weak K-contact manifolds among all weak contact metric manifolds by the property well known for K-contact manifolds, and find when a Riemannian manifold endowed with a unit Killing vector field forms a weak K-contact structure. Second, we find sufficient conditions for a weak K-contact manifold with parallel Ricci tensor or with a generalized Ricci soliton structure to be an Einstein manifold.