Almost complex structure over almost contact metric structures

Articles in Press

Document Type : Original Article

Authors

1 Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran

2 Department of Mathematics, Bijar Branch, Islamic Azad University, Bijar, Iran

Abstract

In this paper, we investigate the conditions under which a lifted almost complex structure ‎‎J‎‎ on the tangent bundle ‎‎TM‎‎ of a manifold ‎‎M‎‎ exhibits various Kählerian properties. We establish several characterizations relating the geometry of ‎‎(TM,J)‎‎ to the cosymplectic structure on ‎‎M‎‎. Specifically, we show that ‎‎(TM,J)‎‎ is Kählerian if and only if ‎‎(M,η,ξ,φ)‎‎ is cosymplectic and ‎‎R=0‎‎. Similarly, we prove that ‎‎(TM,J)‎‎ is nearly Kählerian under the same conditions on ‎‎M‎‎. Furthermore, we present an alternative criterion for ‎‎(TM,J)‎‎ to be Kählerian, involving a nearly cosymplectic condition on ‎‎M‎‎ alongside a specific curvature relation. Finally, we demonstrate that ‎‎(TM,J)‎‎ is semi-Kählerian if and only if ‎‎(M,η,ξ,φ)‎‎ is semi-cosymplectic with ‎‎R(X,Y)φZ=0‎‎. These results reveal intricate connections between cosymplectic structures on ‎‎M‎‎ and Kählerian-type structures on ‎‎TM‎‎, contributing to the broader understanding of almost complex geometry on tangent bundles.

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AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 22 December 2024

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