Turkish Journal of Mathematics
Abstract
E. M. Patterson and K. Yano studied vertical and complete lifts of tensor fields and connections from a manifold M_n to its cotangent bundle T^{\ast} (M_n). Afterwards, K. Yano studied the behavior on the cross-section of the lifts of tensor fields and connections on a manifold M_n to T^{\ast} (M_n) and proved that when \varphi defines an integrable almost complex structure on M_n, its complete lift ^C \varphi is a complex structure. The main result of the present paper is the following theorem: Let \varphi be an almost complex structure on a Riemannian manifold M_n. Then the complete lift ^C \varphi of \varphi, when restricted to the cross-section determined by an almost analytic 1-form \omega on M_n, is an almost complex structure.
DOI
10.3906/mat-0901-31
Keywords
Almost complex structure, cotangent bundle, cross-section, Nijenhuis tensor, analytic tensor field
First Page
487
Last Page
492
Recommended Citation
SALİMOV, A, GEZER, A, & ASLANCI, S (2011). On almost complex structures in the cotangent bundle. Turkish Journal of Mathematics 35 (3): 487-492. https://doi.org/10.3906/mat-0901-31
