Quarter-symmetric connection on an almost Hermitian manifold and on a Kähler manifold

The paper observes an almost Hermitian manifold as an example of a generalized Riemannian manifold and examines the application of a quarter-symmetric connection on the almost Hermitian manifold. The almost Hermitian manifold with quarter-symmetric connection preserving the generalized Riemannian metric is actually the K & auml;hler manifold. Observing the six linearly independent curvature tensors with respect to the quarter- symmetric connection, we construct tensors that do not depend on the quarter-symmetric connection generator. One of them coincides with the Weyl projective curvature tensor of symmetric metric g. Also, we obtain the relations between the Weyl projective curvature tensor and the holomorphically projective curvature tensor. Moreover, we examine the properties of curvature tensors when some tensors are hybrid.