Notes on operators, integrability and the purity conditions of the Sasakian metric according to the almost paracomplex structure in T (Mn)

Asl M. B., Çayir H.

Transactions Issue Mathematics, Azerbaijan National Academy of Sciences, vol.42, no.4, pp.29-37, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 4
  • Publication Date: 2022
  • Journal Name: Transactions Issue Mathematics, Azerbaijan National Academy of Sciences
  • Journal Indexes: Scopus
  • Page Numbers: pp.29-37
  • Keywords: Complete Lift, F −structure, Integrability, Sasakian metric, Tachibana Operators, Tangent Bundle
  • Karadeniz Technical University Affiliated: No

Abstract

© 2022, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.There are different structures in tangent and cotangent bundle. One of them is the complete lifts of the F (K, −(−)K+1)−structure. Firstly, the F (K, −(−)K+1)−structure studyed in Mn to T (Mn) by L. S. Das [8]. The purpose of this paper firstly is to obtain integrability conditions of the almost product (paracomplex) structure ˜ψ= 2 (−) K+1(FK−1) C − I for the condition (FK)C − (−) K+1FC = 0. Later, we get the results of the Tachibana operators applied to vector fields according to the almost product structure ˜ψ on tangent bundle T(Mn). Finally, we have studied the purity conditions of Sasakian metric with respect to the structure ˜ψ..