A generalization of K-contact and (k, μ)-contact manifolds

Abstract

We study a generalization of K-contact and (k, μ)-contact manifolds, and show that if such manifolds of dimensions ≥ 5 are conformally flat, then they have constant curvature +1. We also show under certain conditions that such manifolds admitting a non-homothetic closed conformal vector field are isometric to a unit sphere. Finally, we show that such manifolds with parallel Ricci tensor are either Einstein, or of zero $${\xi}$$ -sectional curvature.