Some results on (<i>k</i>,<i>μ</i>)′ - almost Kenmotsu manifolds

Abstract

In this paper, we study the Weyl conformal curvature tensor W and the concircular curvature tensor C on a (k, μ)′-almost Kenmotsu manifold M²ⁿ⁺¹ of dimension greater than 3. We obtain that if M²ⁿ⁺¹ satisfies either R^.W = 0 or C^.C = 0, then it is locally isometric to either the hyperbolic space H²ⁿ⁺¹(-1) or the Riemannian product Hⁿ⁺¹(-4) x Rⁿ.

Keywords: Almost Kenmotsu manifold, (k, μ)′-nullity distribution, Weyl curvature tensor, concircular curvature tensor