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Indexed by:期刊论文

Date of Publication:2018-01-01

Journal:FILOMAT

Included Journals:SCIE

Volume:32

Issue:1

Page Number:197-206

ISSN No.:0354-5180

Key Words:Almost Kenmotsu 3-manifold; generalized (kappa, mu)'-nullity condition; symmetry condition

Abstract:In this paper, a three-dimensional almost Kenmotsu manifold M-3 satisfying the generalized (kappa, mu)'-nullity condition is investigated. We mainly prove that onM(3) the following statements are equivalent: (1) M-3 is phi-symmetric; (2) the Ricci tensor of M-3 is cyclic-parallel; (3) the Ricci tensor of M-3 is of Codazzi type; (4) M-3 is conformally flat with scalar curvature invariant along the Reeb vector field; (5) M-3 is locally isometric to either the hyperbolic space H-3(-1) or the Riemannian product H-2(-4) x R.