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Almost complex structure over almost contact metric structures | ||
| AUT Journal of Mathematics and Computing | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 02 دی 1403 | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2024.23677.1285 | ||
| نویسنده | ||
| Akbar Sadighi* | ||
| Department of Mathematics, Tabriz Branch Islamic Azad University, Tabriz, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Almost complex structure؛ Cosymplectic structure؛ Nearly cosymplectic structures؛ Kählerian manifolds | ||
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آمار تعداد مشاهده مقاله: 17 |
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