A CLASS OF β-KENMOTSU MANIFOLD ADMITTING GENERALIZED TANAKA-WEBSTER CONNECTION

The objective of this paper is to investigate a class of β-Kenmotsu manifold admitting generalized Tanaka-Webster connection. We use the connection ∇e toinvestigate some curvature properties in the manifold. Here we study the projectiveand ζ-projectively flat curvature tensors admitting the connection ∇e in the manifold.Further, we discuss recurrent condition, conharmonic curvature tensor and Weyl conformal curvature tensor in the manifold admitting the connection ∇e. Likewise, wedemonstrate Ricci pseudo-symmetric, quasi-concircularly flat and ζ-quasi-concircularlyflat β-Kenmotsu manifold admitting the connection ∇e. Finally, we give an example ofa β-Kenmotsu manifold admitting the connection ∇e which support our results.