AUT Journal of Mathematics and Computing

AUT Journal of Mathematics and Computing

Almost complex structure over almost contact metric structures

Document Type : Original Article

Authors
Akbar Sadighi 1
Seyyed Mohammad Zamanzadeh 2
1 Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
2 Department of Mathematics, Bijar Branch, Islamic Azad University, Bijar, Iran
10.22060/ajmc.2024.23677.1285
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 $(M, \eta, \xi, \varphi)$ 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.
Keywords
Almost complex structure
Cosymplectic structure
Nearly cosymplectic structures
Kä
hlerian manifolds
Subjects
[1] M. Ahmad and J.-B. Jun, On semi-invariant submanifolds of a nearly Kenmotsu manifold with a quarter symmetric non-metric connection, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math., 18 (2011), pp. 1–11.
[2] D. E. Blair and J. A. Oubi˜na, Conformal and related changes of metric on the product of two almost contact metric manifolds, Publ. Mat., 34 (1990), pp. 199–207.
[3] H. Faraji, B. Najafi Saghezchi, and T. Tabatabaeifar, k-contact generalized square Finsler manifolds, AUT J. Math. Com., 5 (2024), pp. 329–336.
[4] N. Heidari, N. H. P. Kashani, and B. Najafi, Nearly K¨ahler and nearly Kenmotsu manifolds, Turk. J. Math., 42 (2018), pp. 967–976.
[5] J. JAE-BOK, D. U. CHAND, and P. GOUTAM, On Kenmotso manifolds, J. Korean Math. Soc., 42 (2005), pp. 435–445.
[6] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. (2), 24 (1972), pp. 93–103.
[7] J.-S. Kim, X. Liu, and M. M. Tripathi, On semi-invariant submanifolds of nearly trans-Sasakian manifolds, Int. J. Pure Appl. Math. Sci., 1 (2004), pp. 15–34.
[8] H. Levy, Symmetric tensors of the second order whose covariant derivatives vanish, Ann. of Math. (2), 27 (1925), pp. 91–98.
[9] B. Najafi and N. Hosseinpour Kashani, On nearly Kenmotsu manifolds, Turkish J. Math., 37 (2013), pp. 1040–1047.
[10] A. Sardar, U. C. De, and B. Najafi, 3-dimensional f -Kenmotsu manifolds and solitons, Int. J. Geom. Methods Mod. Phys., 19 (2022), pp. Paper No. 2250199, 15.
[11] S. Sasaki, Almost contact manifolds, Part 2. Lecture Notes, Mathematical Institute, Tohoku University, 1967.
[12] A. Shukla, Nearly trans-Sasakian manifolds, Kuwait J. Sci. Engrg., 23 (1996), pp. 139–144.
[13] T. Takahashi, Sasakian ϕ-symmetric spaces, Tohoku Math. J. (2), 29 (1977), pp. 91–113.
[14] S. Uddin, V. A. Khan, and K. A. Khan, Warped product submanifolds of a Kenmotsu manifold, Turkish J. Math., 36 (2012), pp. 319–330.
AUT Journal of Mathematics and Computing
Volume 7, Issue 2
2026
Pages 183-188