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 $(M, \eta, \xi, \varphi)$ 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 $(M, \eta, \xi, \varphi)$ is semi-cosymplectic with $R(X, Y) \varphi Z = 0$. 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.
Sadighi, A. (2024). Almost complex structure over almost contact metric structures. AUT Journal of Mathematics and Computing, (), -. doi: 10.22060/ajmc.2024.23677.1285
MLA
Sadighi, A. . "Almost complex structure over almost contact metric structures", AUT Journal of Mathematics and Computing, , , 2024, -. doi: 10.22060/ajmc.2024.23677.1285
HARVARD
Sadighi, A. (2024). 'Almost complex structure over almost contact metric structures', AUT Journal of Mathematics and Computing, (), pp. -. doi: 10.22060/ajmc.2024.23677.1285
CHICAGO
A. Sadighi, "Almost complex structure over almost contact metric structures," AUT Journal of Mathematics and Computing, (2024): -, doi: 10.22060/ajmc.2024.23677.1285
VANCOUVER
Sadighi, A. Almost complex structure over almost contact metric structures. AUT Journal of Mathematics and Computing, 2024; (): -. doi: 10.22060/ajmc.2024.23677.1285
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