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

Authors : Milan Lj Zlatanovic, Miroslav Maksimovic

Pages : 963-980

Doi:10.15672/hujms.1219762

View : 149 | Download : 192

Publication Date : 2024-08-27

Article Type : Research Paper

Abstract :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 Kähler 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.
Keywords : Almost Hermitian manifold, curvature tensors, hybrid tensor, K\\\ a hler manifold, quarter symmetric connection, torsion tensor