Quarter-symmetric metric connection in a Kenmotsu manifold. (English) Zbl 1171.53311

Sular, Sibel; Özgür, Cihan; De, Uday Chand

SUT J. Math. 44, No. 2, 297-306 (2008).

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:

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