Some results on pseudosymmetric normal paracontact metric manifolds

Mehmet Atçeken; Tuğba Mert

doi:10.31801/cfsuasmas.937043

Research Article

Year 2022, Volume: 71 Issue: 4, 1044 - 1058, 30.12.2022

Mehmet Atçeken Tuğba Mert

https://doi.org/10.31801/cfsuasmas.937043

Abstract

References

Boothby, M., Wang, R. C., On contact manifolds, Anna Math, 68 (1958), 421-450.
Sasaki, A., Hatakeyama, Y., On differentiable manifolds with certain structure which are closely related to almost contact structure, Tohoku Math. J., 13 (1961), 281-294.
Tanno, S., The automorphism groups of almost contact Riemannian manfifolds, The Tohoku Math. J., 21 (1969), 21-38. DOI: 10.2748/tmj/1178243031
Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24 (1972), 93-103.
Marero, J. C., Chinea, D., On trans-Sasakian manifolds, Proceedings of the XIV. th Spanish- Portuguese Conference on Mathematics. Uni. La. Laguna, 1(3) (1990), 655-659.
Zamkovoy, S., Nakova, G., The decomposition of almost paracontact metric manifolds in eleven classes revisited, J. Geom., 109(18) (2018). https://doi.org/10.1007/s00022-018-0423-5
Mandal, K., De, U. C., Some curvature properties of paracontact metric manifolds, Advances in Pure and Applied Mathematics, 9(3) (2018), 159-165. https://doi.org/10.1515/apam-2017-0064
Özdemir, N., Aktay, S¸., Solgun, M., Almost paracontact structures obtained from $G^{*}_{2(2)}$ structures, Turkısh Journal of Mathematics, 42(6) (2018), 3025-3033. https://doi.org/10.3906/mat-1706-10
Pandey, H., Kumar, A., Anti-Invariant submanifolds of almost paracontact manifolds, Indian J. Pure Appl. Math., 16(6) (1985), 586-590.
Welyczko, J., On Legendre curves in 3-dimensional normal almost paracontact metric manifolds, Results. Math., 54 (2009), 377-387. DOI 10.1007/s00025-009-0364-2
Pokhariyal, G. P., Mishra, R. S., The curvature tensor and their relativistic significances, II. Yokohoma Mathematical journal, 18 (1970), 105-108.
Ojha, R. H., A note on the M-projective curvature tensor, India J. Pure Applied Math., 8 (1975), 1531-1534.
Li, D., Yin, J., Paracontact metric (κ, μ) manifold satisfying the Miao-Tam equation, Advances in Mathematical Physics, 6 (2021), 1-5. DOI: 10.1155/2021/6687223
Atçeken, M., Yuca, G., Some results on invariant submanifolds of an almost Kenmotsu (κ, μ, ν)-space, Honam Mathematical Journal, 43(4) (2021), 655-665. https://doi.org/10.5831/HMJ.2021.43.4.655
Atçeken, M. Some results on invariant submanifolds of Lorentz para-Kenmotsu manifolds, Korean Journal of Mathematics, 30(1) (2022), 175-185. http://dx.doi.org/10.11568/kjm.2022.30.1.175
Atçeken, M., Mert, T., Characterizations for totally geodesic submanifolds of a K-paracontact manifold, AIMS Math., 6(7) (2021), 7320-7332. http://dx.doi.org/10.3934/math.2021430
Mert, T., Characterization of some special curvature tensor on almost $C(\alpha)$−manifold, Asian Jour. of Math. and Com. Res., 29(1) (2022), 27-41.
Mert, T., Atçeken, M., Almost $C(\alpha)$−manifold on $W^{*}_0$ −curvature tensor, App. Math. Sciences, 15(15) (2021), 693-703. doi: 10.12988/ams.2021.916556

Some results on pseudosymmetric normal paracontact metric manifolds

Year 2022, Volume: 71 Issue: 4, 1044 - 1058, 30.12.2022

Mehmet Atçeken Tuğba Mert

https://doi.org/10.31801/cfsuasmas.937043

Abstract

In this article, the M-projective and Weyl curvature tensors on a normal paracontact metric manifold are discussed. For normal paracontact metric manifolds, pseudosymmetric cases are investigated and some interesting results are obtained. We show that a semisymmetric normal paracontact manifold is of constant sectional curvature. We also obtain that a pseudosymmetric normal paracontact metric manifold is an $η$ -Einstein manifold. Finally, we support our topic with an example.

Keywords

M-projective curvature tensor, Weyl curvature tensor, Einstein manifold, $\eta$-Einstein manifold

References

Boothby, M., Wang, R. C., On contact manifolds, Anna Math, 68 (1958), 421-450.
Sasaki, A., Hatakeyama, Y., On differentiable manifolds with certain structure which are closely related to almost contact structure, Tohoku Math. J., 13 (1961), 281-294.
Tanno, S., The automorphism groups of almost contact Riemannian manfifolds, The Tohoku Math. J., 21 (1969), 21-38. DOI: 10.2748/tmj/1178243031
Kenmotsu, K., A class of almost contact Riemannian manifolds, Tohoku Math. J., 24 (1972), 93-103.
Marero, J. C., Chinea, D., On trans-Sasakian manifolds, Proceedings of the XIV. th Spanish- Portuguese Conference on Mathematics. Uni. La. Laguna, 1(3) (1990), 655-659.
Zamkovoy, S., Nakova, G., The decomposition of almost paracontact metric manifolds in eleven classes revisited, J. Geom., 109(18) (2018). https://doi.org/10.1007/s00022-018-0423-5
Mandal, K., De, U. C., Some curvature properties of paracontact metric manifolds, Advances in Pure and Applied Mathematics, 9(3) (2018), 159-165. https://doi.org/10.1515/apam-2017-0064
Özdemir, N., Aktay, S¸., Solgun, M., Almost paracontact structures obtained from $G^{*}_{2(2)}$ structures, Turkısh Journal of Mathematics, 42(6) (2018), 3025-3033. https://doi.org/10.3906/mat-1706-10
Pandey, H., Kumar, A., Anti-Invariant submanifolds of almost paracontact manifolds, Indian J. Pure Appl. Math., 16(6) (1985), 586-590.
Welyczko, J., On Legendre curves in 3-dimensional normal almost paracontact metric manifolds, Results. Math., 54 (2009), 377-387. DOI 10.1007/s00025-009-0364-2
Pokhariyal, G. P., Mishra, R. S., The curvature tensor and their relativistic significances, II. Yokohoma Mathematical journal, 18 (1970), 105-108.
Ojha, R. H., A note on the M-projective curvature tensor, India J. Pure Applied Math., 8 (1975), 1531-1534.
Li, D., Yin, J., Paracontact metric (κ, μ) manifold satisfying the Miao-Tam equation, Advances in Mathematical Physics, 6 (2021), 1-5. DOI: 10.1155/2021/6687223
Atçeken, M., Yuca, G., Some results on invariant submanifolds of an almost Kenmotsu (κ, μ, ν)-space, Honam Mathematical Journal, 43(4) (2021), 655-665. https://doi.org/10.5831/HMJ.2021.43.4.655
Atçeken, M. Some results on invariant submanifolds of Lorentz para-Kenmotsu manifolds, Korean Journal of Mathematics, 30(1) (2022), 175-185. http://dx.doi.org/10.11568/kjm.2022.30.1.175
Atçeken, M., Mert, T., Characterizations for totally geodesic submanifolds of a K-paracontact manifold, AIMS Math., 6(7) (2021), 7320-7332. http://dx.doi.org/10.3934/math.2021430
Mert, T., Characterization of some special curvature tensor on almost $C(\alpha)$−manifold, Asian Jour. of Math. and Com. Res., 29(1) (2022), 27-41.
Mert, T., Atçeken, M., Almost $C(\alpha)$−manifold on $W^{*}_0$ −curvature tensor, App. Math. Sciences, 15(15) (2021), 693-703. doi: 10.12988/ams.2021.916556

There are 18 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	Mehmet Atçeken 0000-0002-1242-4359 Tuğba Mert 0000-0001-8258-8298
Publication Date	December 30, 2022
Submission Date	May 13, 2021
Acceptance Date	May 18, 2022
Published in Issue	Year 2022 Volume: 71 Issue: 4

Cite

APA	Atçeken, M., & Mert, T. (2022). Some results on pseudosymmetric normal paracontact metric manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(4), 1044-1058. https://doi.org/10.31801/cfsuasmas.937043
AMA	Atçeken M, Mert T. Some results on pseudosymmetric normal paracontact metric manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2022;71(4):1044-1058. doi:10.31801/cfsuasmas.937043
Chicago	Atçeken, Mehmet, and Tuğba Mert. “Some Results on Pseudosymmetric Normal Paracontact Metric Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 4 (December 2022): 1044-58. https://doi.org/10.31801/cfsuasmas.937043.
EndNote	Atçeken M, Mert T (December 1, 2022) Some results on pseudosymmetric normal paracontact metric manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 4 1044–1058.
IEEE	M. Atçeken and T. Mert, “Some results on pseudosymmetric normal paracontact metric manifolds”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 4, pp. 1044–1058, 2022, doi: 10.31801/cfsuasmas.937043.
ISNAD	Atçeken, Mehmet - Mert, Tuğba. “Some Results on Pseudosymmetric Normal Paracontact Metric Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/4 (December 2022), 1044-1058. https://doi.org/10.31801/cfsuasmas.937043.
JAMA	Atçeken M, Mert T. Some results on pseudosymmetric normal paracontact metric manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:1044–1058.
MLA	Atçeken, Mehmet and Tuğba Mert. “Some Results on Pseudosymmetric Normal Paracontact Metric Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 4, 2022, pp. 1044-58, doi:10.31801/cfsuasmas.937043.
Vancouver	Atçeken M, Mert T. Some results on pseudosymmetric normal paracontact metric manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(4):1044-58.