Korean J. Math. Vol. 32 No. 4 (2024) pp.593-614
DOI: https://doi.org/10.11568/kjm.2024.32.4.593

On classes of indefinite β-Kenmotsu statistical manifold

Article Sidebar

PDF
Published: Dec 30, 2024
Keywords:
Lightlike hypersurfaces, leaves, indefinite nearly β-Kenmotsu statistical manifold
Mathematics Subject Classification:
53D10, 53D15, 58A05, 58B20

Main Article Content

Shagun Bhatti
Department of Mathematics, Punjabi University, Patiala, Punjab, India 147002.
https://orcid.org/0000-0002-8734-5508
Jasleen Kaur
Department of Mathematics, Punjabi University, Patiala, Punjab, India 147002.
https://orcid.org/0000-0002-4284-2842

Abstract

This paper introduces the notion of lightlike hypersurfaces for a novel class of manifolds known as an indefinite nearly β-Kenmotsu statistical manifold and explores the associated geometric properties. It establishes results on the screen totally geodesic and screen totally umbilical lightlike hypersurfaces. It delineates the structure of the recurrent, Lie-recurrent and nearly recurrent structure tensor fields of lightlike hypersurfaces of an indefinite nearly β−Kenmotsu statistical manifold. Additionally, the geometry of leaves of integrable distributions of lightlike hypersurfaces in an indefinite β-Kenmotsu statistical manifold tangent to the structure vector field has been researched.



Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.

References

[1] M. Ahmad and J. B. Jun, On semi-invariant submanifolds of a nearly Kenmotsu manifold with a semi-symmetric non-metric connection, J. Chungcheong Math. Soc. 23 (2) (2010), 257–257. https://dx.doi.org/10.14403/jcms.2010.23.2.257 Google Scholar

[2] S. Amari, Differential-geometrical methods in statistics, Lecture Notes in Statistics, New York, Springer, 1985. Google Scholar

[3] S. I. Amari, O. E. Barndorff-Nielsen, R. E. Kass, S. L. Lauritzen and C. R. Rao, Differential geometry in statistical inference, 1987. Google Scholar

[4] M. Atceken and S. Dirik, Pseudo-slant submanifolds of nearly Kenmotsu manifold, Serdica Math. J. 41 (2-3) (2015), 243–262. Google Scholar

[5] O. Bahadr, On lightlike geometry of indefinite Sasakian statistical manifolds, AIMS Math. 6 (11) (2021), 12845–12862. https://dx.doi.org/10.3934/math.2021741 Google Scholar

[6] O. Bahadr, A. N. Siddiqui, M. Glbahar and A. H. Alkhaldi, Main curvatures identities on lightlike hypersurfaces of statistical manifolds and their characterizations, Mathematics 10 (13) (2022), 2290. https://dx.doi.org/10.3390/math10132290 Google Scholar

[7] O. Bahadr and M. M. Tripathi, Geometry of lightlike hypersurfaces of a statistical manifold, WSEAS Trans. Math. 22 (2023), 466–474. https://dx.doi.org/10.37394/23206.2023.22.52 Google Scholar

[8] N. Behzad and N. H. Kashani, On nearly Kenmotsu manifolds, Turk. J. Math. 37 (6) (2013), 1040–1047. https://dx.doi.org/10.3906/mat-1207-38 Google Scholar

[9] S. Bhatti and J. Kaur, Contact CR and SCR lightlike submanifolds of an indefinite Kenmotsu statistical manifold, arXiv:2303.17194v1, 30 Mar 2023. https://dx.doi.org/10.48550/arXiv.2303.17194 Google Scholar

[10] D. Chinea and C. Gonzalez, A classification of almost contact metric manifolds, Ann. Mat. Pura Appl. 156 (1990), 15–36. Google Scholar

[11] K. L. Duggal and A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds and applications, Dordrecht, Kluwer Academic, 1996. https://dx.doi.org/10.1007/978-94-017-2089-2 Google Scholar

[12] K. L. Duggal and B. Sahin, Differential Geometry of Lightlike Submanifolds, Springer Science & Business Media, 2011. Google Scholar

[13] H. Furuhata, Hypersurfaces in statistical manifolds, Differ. Geom. Appl. 27 (3) (2009), 420–429. https://dx.doi.org/10.1016/j.difgeo.2008.10.019 Google Scholar

[14] H. Furuhata, I. Hasegawa, Y. Okuyama and K. Sato, Kenmotsu statistical manifolds and warped product, J. Geom. 108 (3) (2017), 1175–1191. https://dx.doi.org/10.1007/s00022-017-0403-1 Google Scholar

[15] H. Furuhata, I. Hasegawa, Y. Okuyama, K. Sato and M. H. Shahid, Sasakian statistical manifolds, J. Geom. Phys. 117 (2017), 179–186. https://dx.doi.org/10.1016/j.geomphys.2017.03.010 Google Scholar

[16] C. Gherghe, Harmonicity on nearly trans-Sasaki manifolds, Demonstr. Math. 33 (1) (2000), 151–157. https://dx.doi.org/10.1515/dema-2000-0118 Google Scholar

[17] D. H. Jin, Lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a non-metric φ-symmetric connection, Bull. Korean Math. Soc. 53 (6) (2016), 1771–1783. https://dx.doi.org/10.4134/BKMS.b150972 Google Scholar

[18] D. H. Jin, Lightlike hypersurfaces of an indefinite nearly trans-Sasakian manifold, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 2 (2019), 195–210. Google Scholar

[19] T. Khan, On non-invariant hypersurfaces of a nearly Kenmotsu manifold, IOSR-JM 15 (6) (2019), 30–34. Google Scholar

[20] S. L. Lauritzen, Statistical manifolds, Differential geometry in statistical inference 10 (1987), 163–216. https://dx.doi.org/10.1214/lnms/1215467061 Google Scholar

[21] F. Massamba, On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds, J. Geom. 95 (2009), 73–89. https://dx.doi.org/10.1007/s00022-010-0021-7 Google Scholar

[22] F. Massamba, Lightlike geometry of leaves in indefinite Kenmotsu manifolds, CUBO 13 (3) (2011), 69–89. https://dx.doi.org/10.2478/s12175-012-0012-2 Google Scholar

[23] F. Massamba, Lightlike hypersurfaces in indefinite trans-Sasakian manifolds, Results Math. 63 (1-2) (2013), 251–287. https://dx.doi.org/10.1007/s00025-011-0197-7 Google Scholar

[24] J. A. Oubina, New class of almost contact metric structure, Publ. Math. Debr. 32 (1985), 187–193. Google Scholar

[25] V. Rani and J. Kaur, On the structure of lightlike hypersurfaces of an indefinite Kaehler statistical manifold, Differ. Geom.-Dyn. Syst. 23 (2021), 221–234. Google Scholar

[26] A. N. Shukla, Nearly trans-Sasakian manifolds, KJSE 23 (1996), 139–144. Google Scholar

[27] E. Yasar, A. C. Coeken and A. Yuecesan, Lightlike hypersurfaces of semi-Riemannian manifold with semi-symmetric metric connection, KJSE 34 (2007), 11–24. Google Scholar