Onthe geometry of an almost α-cosymplectic (k, µ, ν)-spaces

Pakize Uygun; Mehmet Atçeken; Tugba  Mert

doi:10.59400/jam.v2i4.206

Onthe geometry of an almost α-cosymplectic (k, µ, ν)-spaces

Pakize Uygun Department of Mathematics, Faculty of Arts and Sciences, Aksaray University, 68100 Aksaray, Turkey
Mehmet Atçeken Department of Mathematics, Faculty of Arts and Sciences, Aksaray University, 68100 Aksaray, Turkey
Tugba Mert Department of Mathematics, Faculty of Sciences, Sivas Cumhuriyet University, 58140 Sivas, Turkey

Ariticle ID: 206

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DOI: https://doi.org/10.59400/jam.v2i4.206

Keywords: α-cosymplectic (k,µ,ν)-spaces; W6-curvaturetensor; W9-curvature tensor

Abstract

The object of the paper is to investigate almost α-cosymplectic (k,µ,ν)-spaces. Some results on almost cosymplectic (k,µ,ν)-spaces with certain conditions are obtained.

References

[1] Dacko P, Olszak Z. On almost cosymplectic (k, µ, ν)−spaces. Banach Center Publications 2005; 69(1): 211–220.

[2] Dacko P, Olszak Z. On almost cosymplectic (−1, µ, σ)−spaces. Central European Journal of Math. CEJM 2005; 3(2): 318–330.

[3] Boeckx E. Afull classification of contact metric (k, µ)−spaces. Illinois J. Math. 2000; 44(1): 212–219.

[4] Goldberg SI, Yano K. Integrability of almost cosymplectic strustures. Pcific J. Math. 1969; 31: 373–382.

[5] Ozturk H, Aktan N, Murathan C. Almost α−cosymplectic (k, µ, ν)−spaces. arXiv 2010; 1077: 0527 v1.

[6] Atçeken M. Characterizations for an invariant submanifold of an almost α−cosymplectic (k, µ, ν)−space to be totally geodesic. Filomat 2022; 36(9): 2871–2879.

[7] Carriazo A, Martin-Molina V. Almost cosymplectic and almost Kenmotsu (k, µ, ν)−space, Mediterr. J. Math. 2013; 10: 1551–1571.

[8] Kim TW,Pak HK. Canonical foliations of certain classses of almost contact metric structures. Acta Mathematica Sinica. English Series 2005; 21(4): 841–856.

[9] Yolda HI. Some results on α−cosymplectic manifolds. Bull. Transil. Univ. Brasov Sene III. Math. Comput. Sci. 2021; (1): 15–128.

[10] Yolda HI. Some results on cosymplectic manifolds admitting certain vector fields. J. Geom. Symmetry Phys. 2021; 60: 83–94.

[11] Yolda HI. On some classes of generalized recurrent α-cosymplectic manifolds. Turk. J. Math. Computer Sci. 2022; 14(1), 74–81.

[12] Aktan N, Balkan S, Yildirim M. On weakly symmetries of almost Kenmotsu (k, µ, ν)−spaces. Hacettepe J. Math. Stat. 2013; 42(4): 447–453.

[13] Koufogiorgos T, Markellos M, Papantoniou VJ. The harmonicity of the Reeb vector fields on contact 3-manifolds. Pasific J. Math. 2008; 234(2): 325–344.

[14] Pokhariyal GP. Relativistic significance of curvature tensors. Internat. J. Math. Sci. 1982; 5(1): 133–139.

[15] Blair DE, Koufogiorgos T, Papantoniou BJ. Contact metric manifolds satisfying a nullity condition. Israel J. Math. 1995; 91: 189–214.

[16] Küpeli Erken I. On a classıfıcation of almost α−cosymplectic manifolds. Khayyam Journal of Math. 2019; 5(1):1–10.

[17] Olszak Z. On almost cosymplectic manifolds. Kodai Math. J. 1981; 4: 239–250.

[18] Yano K, Bochner S. Curvature and Betti numbers, Annals of Mathematics Studies 32. Princeton University Press; 1953.

Published

2024-09-09

How to Cite

Uygun, P., Atçeken, M., & Mert, T. (2024). Onthe geometry of an almost α-cosymplectic (k, µ, ν)-spaces. Journal of AppliedMath, 2(4), 206. https://doi.org/10.59400/jam.v2i4.206

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Vol. 2 No. 4 (2024)

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Commentary

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