BI-TANGENT QUATERNION KAEHLER MANIFOLDS

Complex structures and tangent structures are well known. Almost semi-quaternion manifolds formed by the combination of these two structures have been also studied. In this paper, firstly, the existence of a structure similar to the quaternion Kaehler manifold for an almost semi-quaternion manifold is investigated. For this purpose, the necessary conditions are obtained for the covariant derivative of each cross-section to remain in the vector bundle formed by these cross-sections. After this stage, the interactions of these cross-sections and the curvature tensor field are investigated. In this direction, new relations were found. Finally, the flatness of the manifolds with this type of structure in case of constant curvature is examined. © 2024, Politechnica University of Bucharest. All rights reserved.