Some important notes on an almost α-cosymplectic (k, µ, ν)-manifolds

Pakize Uygun

doi:10.59400/jam.v1i4.202

Some important notes on an almost α-cosymplectic (k, µ, ν)-manifolds

Pakize Uygun Department of Mathematics, Faculty of Arts and Sciences, Aksaray University, Aksaray 68100, Turkey

Ariticle ID: 202

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DOI: https://doi.org/10.59400/jam.v1i4.202

Keywords: α-cosymplectic (k, μ, ν)-manifolds;W3-curvature tensor; W4-curvature tensor

Abstract

The current work looks at certain geometric requirements that must be satisfied for an invariant submanifold of an almost α- cosymplectic (k, µ, ν)-manifolds to be totally geodesic. Consequently, we obtain some interesting results invariant submanifolds of an almost cosymplectic (k, µ, ν)-manifolds. Additionally, we give an example on 5-dimensional case.

References

Olszak Z. On almost cosymplectic manifolds. Kodai Mathematical Journal. 1981; 4(2).

doi: https://doi.org/10.2996/kmj/1138036371

Goldberg S, Yano K. Integrability of almost cosymplectic structures. Pacific Journal of Mathematics. 1969; 31(2): 373-382. doi: https://doi.org/10.2140/pjm.1969.31.373

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

Atçeken M. Characterizations for an invariant submanifold of an almost α-cosymplectic (κ,μ,ν)-space to be totally geodesic. Filomat. 2022; 36(9): 2871-2879. doi: https://doi.org/10.2298/fil2209871a

Aktan N,Balkan S, Yildirim M. On weakly symmetries of almost Kenmotsu (k, µ, ν)−spaces.Hacettepe Journal of Mathematics and Statistics. 2013; 42 (4): 447-453.

Blair DE, Koufogiorgos T, Papantoniou BJ. Contact metric manifolds satisfying a nullity condition. Israel Journal of Mathematics. 1995; 91(1-3): 189-214. doi: https://doi.org/10.1007/bf02761646

Boeckx E. A full classification of contact metric (k, µ)-spaces. Illinois Journal of Mathematics. 2000; 44(1). doi: https://doi.org/10.1215/ijm/1255984960

Carriazo A, Martín-Molina V. Almost Cosymplectic and Almost Kenmotsu (κ, μ, ν)-Spaces. Mediterranean Journal of Mathematics. 2013; 10(3): 1551-1571. doi: https://doi.org/10.1007/s00009-013-0246-4

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

Dacko P, Olszak Z. On almost cosymplectic (−1, μ, 0)-spaces. Central European Journal of Mathematics. 2005; 3(2): 318-330. doi: https://doi.org/10.2478/bf02479207

Kim TW, Pak HK. Canonical Foliations of Certain Classes of Almost Contact Metric Structures. Acta Mathematica Sinica, English Series. 2005; 21(4): 841-846.

doi: https://doi.org/10.1007/s10114-004-0520-2

Koufogiorgos T, Markellos M, Papantoniou V. The harmonicity of the Reeb vector field on contact metric 3-manifolds. Pacific Journal of Mathematics. 2008; 234(2): 325-344.

doi: https://doi.org/10.2140/pjm.2008.234.325

Mert T, Atçeken M. A note on pseudoparallel submanifolds of Lorentzian para-Kenmotsu manifolds. Filo- mat.2023; 37(15): 5095-5107.

Mert T, Atçeken M. Some important properties of almost Kenmotsu (k, µ, ν)−space on the concircular curvature tensor. Fundamental journal of mathematics and applications (Online) . 2023; 6(1): 51-60.

Mert T, et al.On Invariant submanifolds of Lorentz Sasakian space forms. Journal of Mathematical Exten- sion 2023; 17(3): 1–17.

Ozturk H, Aktan N, Murathan C. Almost α−cosymplectic (k, µ, ν)−spaces, ArXiv: 10077. 0527 v1.

Pokhariyal GP, Mishra RS. Curvature tensors and their relativistic significance II. Yokohama Mathematical Journal. 1971; 19 (2): 97-103.

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

Published

2023-12-15

How to Cite

Uygun, P. (2023). Some important notes on an almost α-cosymplectic (k, µ, ν)-manifolds. Journal of AppliedMath, 1(4), 202. https://doi.org/10.59400/jam.v1i4.202

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