On a Semi-symmetric Metric Connection in an Almost Kenmotsu Manifold with Nullity Distributions

Ghosh, Gopal ; De, Uday Chand

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 55 (2016) no. 2, pp. 87-99.

Résumé

We consider a semisymmetric metric connection in an almost Kenmotsu manifold with its characteristic vector field $\xi $ belonging to the $(k,\mu )^{\prime }$-nullity distribution and $(k,\mu )$-nullity distribution respectively. We first obtain the expressions of the curvature tensor and Ricci tensor with respect to the semisymmetric metric connection in an almost Kenmotsu manifold with $\xi $ belonging to $(k,\mu )^{\prime }$- and $(k,\mu )$-nullity distribution respectively. Then we characterize an almost Kenmotsu manifold with $\xi $ belonging to $(k,\mu )^{\prime }$-nullity distribution admitting a semisymmetric metric connection.

Détail

Classification : 53C25, 53C35
Keywords: Semisymmetric metric connection; almost Kenmotsu manifold; Einstein manifold; sectional curvature; Ricci tensor; Weyl conformal curvature tensor