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Zbl 1171.53311
Sular, Sibel; Özgür, Cihan; De, Uday Chand
Quarter-symmetric metric connection in a Kenmotsu manifold. (English)
[J] SUT J. Math. 44, No. 2, 297-306 (2008). ISSN 0916-5746

Summary: We consider a quarter-symmetric metric connection in a Kenmotsu manifold. We investigate the curvature tensor and the Ricci tensor of a Kenmotsu manifold with respect to the quarter-symmetric metric connection. We show that the scalar curvature of an $n$-dimensional locally symmetric Kenmotsu manifold with respect to the quarter-symmetric metric connection is equal to $n(1-n)$. Furthermore, we obtain the non-existence of generalized recurrent, $\varphi$-recurrent and pseudosymmetric Kenmotsu manifolds with respect to quartersymmetric metric connection.

MSC 2000:: *53C05 Connections, general theory
53D15 Almost contact and almost symplectic manifolds

Keywords: quarter-symmetric metric connection; Kenmotsu manifold; locally symmetric manifold; generalized recurrent manifold; $\varphi$-recurrent manifold; pseudosymmetric manifold

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Zentralblatt MATH Berlin [Germany]