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

Our paper explores warped product pointwise semi-slant submanifolds with a semi-symmetric metric connection in an odd-dimensional sphere and uncovers fundamental results. We also demonstrate how our findings can be applied to the homology of these submanifolds. Notably, we prove that under specific condition, there are no stable currents for This work adds valuable insights into stability behav...