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In this paper, we prove that the Ricci tensor of a three-dimensional almost Kenmotsu manifold satisfying $\nabla_\xi h=0$, $h\neq0$, is $\eta$-parallel if and only if the manifold is locally isometric to either the Riemannian product $\mathbb{H}^{2}(-4)\times\mathbb{R}$ or a non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure.
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참고문헌 (18)
참고문헌 신청
A. M. Pastore / 2011 / Generalized nullity distributions on almost Kenmotsu manifolds / Int. Electron. J. Geom 4 (2) : 168 ~ 183
B. Cappelletti-Montano / 2013 / A survey on cosymplectic geometry / Rev. Math. Phys 25 : 55 ~
D. E. Blair / 1990 / Three dimensional locally symmetric contact metric manifolds / Boll Un. Mat. Ital. A (7) 4 (3) : 385 ~ 390
D. E. Blair / 2010 / Riemannian Geometry of Contact and Symplectic Manifolds / Birkhauser
D. Janssens / 1981 / Almost contact structures and curvature tensors / Kodai Math. J 4 (1) : 1 ~ 27
B. Cappelletti-Montano / 2013 / A survey on cosymplectic geometry / Rev. Math. Phys 25 : 55 ~
D. E. Blair / 1990 / Three dimensional locally symmetric contact metric manifolds / Boll Un. Mat. Ital. A (7) 4 (3) : 385 ~ 390
D. E. Blair / 2010 / Riemannian Geometry of Contact and Symplectic Manifolds / Birkhauser
D. Janssens / 1981 / Almost contact structures and curvature tensors / Kodai Math. J 4 (1) : 1 ~ 27
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