SOME RESEARCH NOTES ON LIFTS OF THE HSU – (4,2) STRUCTURE ON COTANGENT AND TANGENT BUNDLE

There are a lot of structures in tangent and cotangent bundle. One of them is the Hsu – (4,2) structure have been defined and studied by Yano, Hough and Chen [1] and the complete and horizontal lifts of Hsu – (4,2) structure extended in M^n to cotangent bundle by R. Nivas and M. Saxena [2]. Hsu-structure had been defined firstly by Prof Mishra [3]. This paper consists of two main sections. In the first part, we find the integrability conditions by calculating Nijenhuis tensors of the complete and horizontal lifts of Hsu – (4,2) structure. Later, we get the results of Tachibana operators applied to vector and covector fields according to the complete and horizontal lifts of Hsu – (4,2) structure and the conditions of almost holomorfic vector fields in cotangent bundle T^* (M^n ). Finally, we have studied the purity conditions of Sasakian metric with respect to the lifts of Hsu – (4,2) structure. In the second part, all results obtained in the first section were investigated according to the complete and horizontal lifts of the Hsu – (4,2) structure in tangent bundle T^* (M^n ).