Journal of the
Korean Mathematical Society JKMS

The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semi-symmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.

Keywords: Ricci semi-symmetric Kenmotsu manifold, Weyl semi-symmetric Kenmotsu manifold, $\eta$-Einstein manifold, $\eta$-parallel Ricci tensor

MSC numbers: 53C25