We obtain curvature tensor R̃(X, Y )Z w.r.t quarter-symmetric metric connection in terms of curvature tensor R(X,Y )Z relative to the Levi-civita connection in a K-contact manifold. Further, locally φ-symmetric, φ-symmetric and locally projective φ-symmetric K-contact manifolds with respect to the quarter-symmetric metric connection are studied and some results are obtained. The results are assi...

The object of the present paper is to study locally φsymmetric LP-Sasakian manifolds admitting semi-symmetric metric connection and obtain a necessary and sufficient condition for a locally φsymmetric LP-Sasakian manifold with respect to semi-symmetric metric connection to be locally φ-symmetric LP-Sasakian manifold with respect to Levi-Civita connection. AMS Mathematics Subject Classification ...

In this paper, we study Riemannian submersions from a manifold endowed with quarter-symmetric non-metric connection onto manifold. We investigate O’Neill’s tensor fields for and derive the covariant derivative of fields. obtain derivatives those compare curvatures total manifold, base fibers by computing curvatures.

We study the quarter-symmetric metric A-connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to A-connection, we construct Weyl projective tensor In this way, obtain new conditions for manifold be projectively flat. At end of paper, define η-Einstein manifolds θ-th kind and prove that they coincide