Some properties of Kenmotsu manifolds admitting a new type of semi-symmetric non-metric connection.
Keywords:
Kenmotsu manifold, semi-symmetric non-metric connection, semi-symmetric manifold, Ricci semi-symmetric manifold, locallyϕ-symmetric Kenmotsu manifold, curvature tensor, Ricci tensor, Einstein manifold.Abstract
In this paper we study some properties of Kenmotsu manifolds admitting a semi-symmetric non-metric connection. Some curvature's properties of Kenmotsu manifolds that admits a semi-symmetric non-metric connection are obtained. Semi-symmetric, Ricci semi-symmetric and locally $\phi$-symmetric conditions for Kenmotsu manifolds with respect to semi-symmetric non-metric connection are also studied. It is proved that the manifold endowed with a semi-symmetric non-metric connection is regular. We obtain some conditions for semi-symmetric and Ricci semi-symmetric Kenmotsu manifolds endowed with semi-symmetric non-metric connection $\widetilde{\nabla}$. It is further observed that the Ricci soliton of data $(g,\xi,\Theta)$ are expanding and shrinking respectively for semi-symmetric and Ricci semi-symmetric Kenmotsu manifolds admitting a semi-symmetric non-metric connection.
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