SOME RESULTS ON ALMOST KENMOTSU MANIFOLDS WITH GENERALIZED (k, μ)′-NULLITY DISTRIBUTION

In the present paper, we prove that if there exists a second order parallel tensor on an almost Kenmotsu manifold with generalized (k, mu)'-nullity distribution and h' not equal 0, then either the manifold is isometric to Hn+1 (-4) x R-n, or, the second order parallel tensor is a constant multiple of the associated metric tensor of M2n+1 under certain restriction on k, mu. Besides this, we study Ricci soliton on an almost Kenmotsu manifold with generalized (k, mu)'-nullity distribution. Finally, we characterize such a manifold admitting generalized Ricci soliton.