Open AccessSOME RESEARCH NOTES ON LIFTS OF THE HSU – (4,2) STRUCTURE ON COTANGENT AND TANGENT BUNDLE
Author(s) -
Haşim Çayır,
Ahmet Bahadir,
Betül Can Uzun Uzun
Publication year - 2021
Publication title -
journal of science and arts
Language(s) - English
Resource type - Journals
eISSN - 2068-3049
pISSN - 1844-9581
DOI - 10.46939/j.sci.arts-21.3-a14
Subject(s) - cotangent bundle , tangent bundle , mathematics , trigonometric functions , section (typography) , vector bundle , pure mathematics , normal bundle , tangent , frame bundle , bundle , mathematical analysis , geometry , tangent space , computer science , materials science , composite material , operating system
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 ).