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. and Zamanzadeh, S. M. (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. , and Zamanzadeh, S. M. . "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., Zamanzadeh, S. M. (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 and S. M. Zamanzadeh, "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., Zamanzadeh, S. M. 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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