Communications of the
Korean Mathematical Society CKMS

In the present study, we consider some curvature properties of generalized $B$-curvature tensor on Kenmotsu manifold. Here first we describe certain vanishing properties of generalized $B$ curvature tensor on Kenmostu manifold. Later we formulate generalized $B$ pseudo-symmetric condition on Kenmotsu manifold. Moreover, we also characterize generalized $B$ $\phi$-recurrent Kenmotsu manifold.

Keywords: Kenmotsu manifold, generalized $B$ curvature tensor, scalar curvature, $eta$-Einstein manifold

MSC numbers: Primary 53C05, 53C15, 53C25