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Some results on almost Kenmotsu manifolds


Abstract


First we consider almost Kenmotsu manifolds which satisfy Codazzi condition for h and \varphi h, and we prove that in such cases the tensor h vanishes. Next, we prove that an almost Kenmotsu manifold having constant \xi-sectional curvature K which is locally symmetric is a Kenmotsu manifold of constant curvature K=-1. We also prove that, for a (\kappa,\mu)'-almost Kenmotsu manifold of dim>3 with h'\neq 0, every conformal vector field is Killing. Finally, we prove that if M is a (\kappa,\mu)'-almost Kenmotsu manifold with h'\neq 0 and \kappa \neq -2, then the vector field V which leaves the curvature tensor invariant is Killing.

DOI Code: 10.1285/i15900932v40n1p87

Keywords: Almost Kenmotsu manifold; Locally symmetric spaces; Infinitesimal contact transformation; Conformal vector field

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