- International Electronic Journal of Geometry
- Vol: 13 Issue: 1
- On the Integrability Conditions and Operators of the F((K + 1),(K − 1))− Structure Satisfying F K+1 ...
On the Integrability Conditions and Operators of the F((K + 1),(K − 1))− Structure Satisfying F K+1 + F K−1 = 0, (F 6= 0, K 1 2) on Cotangent Bundle and Tangent Bundle
Authors : Lovejoy Das, Haşim Çayir
Pages : 94-106
Doi:10.36890/iejg.559746
View : 7 | Download : 2
Publication Date : 2020-01-30
Article Type : Research
Abstract :This paper consists of two main sections. In the first part, we find the integrability conditions of the horizontal lifts of $F((K+1),(K-1))-$ structure satisfying $F^{K+1}+F^{K-1}=0,$ $(F\neq 0,$ $K\eqslantgtr 2)$. Later, we get the results of Tachibana operators applied to vector and covector fields according to the horizontal lifts of $F((K+1),(K-1))-$structure in cotangent bundle $T^{\ast }(M^{n})$. Finally, we have studied the purity conditions of Sasakian metric with respect to the horizontal lifts of the structure. In the second part, all results obtained in the first section were obtained according to the complete and horizontal lifts of the structure in tangent bundle $T(M^{n})$.Keywords : Integrability conditions, Tachibana operators, $CR-$Submanifolds, $CR-$Stucture, tangent bundle, cotangent bundle