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STCR-Lightlike Product Manifolds of an Indefinite Kaehler Statistical Manifold with a Quarter Symmetric Non-Metric Connection

Year 2022, Volume: 15 Issue: 2, 229 - 241, 31.10.2022

Vandana Rani , Jasleen Kaur

https://doi.org/10.36890/iejg.1130240

Abstract

The present work aims to introduce a novel class of submanifolds, namely STCR-lightlike submanifolds, for an indefinite Kaehler statistical manifold with a quarter symmetric non-metric connection. The characterization theorems on totally umbilical and totally geodesic STCR-lightlike submanifolds with respect to the integrability of distributions have been established. Some conditions for a STCR-lightlike submanifold to be a STCR-lightlike product manifold have been derived.

Keywords

STCR lightlike submanifolds indefinite Kaehler statistical manifold totally geodesic foliation integrability

References

  • [1] Amari, S.: Differential geometrical methods in statistics, Lecture notes in statistics, 28, Springer, New York, 1985.
  • [2] Amari, S.: Differential geometrical theory of statistics, Differential geometry in statistical inference, Institute of Mathematical statistics, Hayward, California, 10 (1987), 19-94.
  • [3] Bahadir, O. and Tripathi, M.M.: Geometry of lightlike hypersurfaces of a statistical manifold, arXiv:1901.092526, 26 Jan 2019.
  • [4] Bahadir, O.: On lightlike geometry of indefinite Sasakian statistical manifolds, arXiv:2004.01512, 10 Mar 2020.
  • [5] Bahadir, O. and Kilic, E.: Lightlike submanifolds of indefinite Kaehler manifolds with quarter symmetric non-metric connection, Mathematical sciences and applications E-notes, 2 (2014), no. 2, 89-104.
  • [6] Bahadir, O. and Kilic, E.: Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection, International electronic journal of geometry, 9 (2016), no. 1, 9-22.
  • [7] Dogan, B., Sahin, B. and Yasar, E.: Screen transversal Cauchy Riemann lightlike submanifolds, Filomat 34:5 (2020), 1581-1599.
  • [8] Duggal, K.L. and Bejancu, A.: Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and its applications, Kluwer Academic, 1996.
  • [9] Duggal, K.L. and Jin, D.H.: Totally umbilical lightlike submanifolds, Kodai Math.J, 26 (2003), 49-68.
  • [10] Duggal, K.L. and Sahin, B.: Screen Cauchy Riemann lightlike submanifolds, Acta Math Hungar, 106 ( 2005), no. (1-2), 137–165.
  • [11] Duggal, K.L. and Sahin, B.: Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds, Acta Mathematica Hungarica, 112 (2006), no.(1-2), 107–130.
  • [12] Furuhata, H. and Hasegawa, I.: Submanifold theory in holomorphic statistical manifolds, Geometry of Cauchy-Riemann submanifolds, Springer, Singapore, 179-215, 2016.
  • [13] Golab, S.:On semi-symmetric and quarter-symmetric linear connections, Tensor, 29(1975), no.3, 249-254.
  • [14] Gupta, G., Kumar, R. and Nagaich, R.K.: Geometry of semi-invariant lightlike product manifolds, New York J.Math, 26 (2020), 1338-1354.
  • [15] Kaur, J. and Rani, V.: Distributions in CR-lightlike submanifolds of an indefinite Kaehler statistical manifold, Malaya Journal of Matematik, 8(2020), no. 4, 1346-1353.
  • [16] Kilic, E. and Bahadir, O.: Lightlike Hypersurfaces of a Semi-Riemannian Product Manifold and Quarter- Symmetric Nonmetric Connections, International Journal of Mathematics and Mathematical Sciences, Volume 2012, Article ID 178390, 17 pages.
  • [17] Milijevic, M.: CR-submanifolds in holomorphic statistical manifolds, Ph.D Thesis in Science, Department of Mathematics Graduates School of Science, Hokkaido University, 2015.
  • [18] Rani, V. and Kaur, J.: Cauchy Riemann-lightlike submanifolds in the aspect of an indefinite Kaehler statistical manifold, Malaya Journal of Matematik, 9(2021), no. 1, 136-143.
  • [19] Rani, V. and Kaur, J.: On structure of lightlike hypersurfaces of an indefinite Kaehler statistical manifold, Differential Geometry-Dynamical Systems, 23 (2021), 221-234.
  • [20] Rao, C.R.: Information and the accuracy attainable in the estimation of statistical parameters, Bulletin of Calcutta Mathematical Society, 37 (1945), 81-91.
  • [21] Sahin, B. and Gunes, R.: Geodesic CR-lightlike submanifolds, Beitrage zur Algebra und Geometrie, Contribution to Algebra and Geometry, 42 (2001), no.2, 583-594.
  • [22] Sahin, B.: Transversal lightlike submanifolds of indefinite Kaehler manifolds, An. Univ. Vest Timis. Ser. Mat.-Inform, 44 (2006),119-145.
  • [23] Sahin, B.: Screen transversal lightlike submanifolds of Kaehler manifolds, Chaos, Solitons and Fractals, 38 (2008),1439-1448.

Year 2022, Volume: 15 Issue: 2, 229 - 241, 31.10.2022

Vandana Rani , Jasleen Kaur

https://doi.org/10.36890/iejg.1130240

Abstract

References

  • [1] Amari, S.: Differential geometrical methods in statistics, Lecture notes in statistics, 28, Springer, New York, 1985.
  • [2] Amari, S.: Differential geometrical theory of statistics, Differential geometry in statistical inference, Institute of Mathematical statistics, Hayward, California, 10 (1987), 19-94.
  • [3] Bahadir, O. and Tripathi, M.M.: Geometry of lightlike hypersurfaces of a statistical manifold, arXiv:1901.092526, 26 Jan 2019.
  • [4] Bahadir, O.: On lightlike geometry of indefinite Sasakian statistical manifolds, arXiv:2004.01512, 10 Mar 2020.
  • [5] Bahadir, O. and Kilic, E.: Lightlike submanifolds of indefinite Kaehler manifolds with quarter symmetric non-metric connection, Mathematical sciences and applications E-notes, 2 (2014), no. 2, 89-104.
  • [6] Bahadir, O. and Kilic, E.: Lightlike Submanifolds of a Semi-Riemannian Product Manifold with Quarter Symmetric Non-Metric Connection, International electronic journal of geometry, 9 (2016), no. 1, 9-22.
  • [7] Dogan, B., Sahin, B. and Yasar, E.: Screen transversal Cauchy Riemann lightlike submanifolds, Filomat 34:5 (2020), 1581-1599.
  • [8] Duggal, K.L. and Bejancu, A.: Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and its applications, Kluwer Academic, 1996.
  • [9] Duggal, K.L. and Jin, D.H.: Totally umbilical lightlike submanifolds, Kodai Math.J, 26 (2003), 49-68.
  • [10] Duggal, K.L. and Sahin, B.: Screen Cauchy Riemann lightlike submanifolds, Acta Math Hungar, 106 ( 2005), no. (1-2), 137–165.
  • [11] Duggal, K.L. and Sahin, B.: Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds, Acta Mathematica Hungarica, 112 (2006), no.(1-2), 107–130.
  • [12] Furuhata, H. and Hasegawa, I.: Submanifold theory in holomorphic statistical manifolds, Geometry of Cauchy-Riemann submanifolds, Springer, Singapore, 179-215, 2016.
  • [13] Golab, S.:On semi-symmetric and quarter-symmetric linear connections, Tensor, 29(1975), no.3, 249-254.
  • [14] Gupta, G., Kumar, R. and Nagaich, R.K.: Geometry of semi-invariant lightlike product manifolds, New York J.Math, 26 (2020), 1338-1354.
  • [15] Kaur, J. and Rani, V.: Distributions in CR-lightlike submanifolds of an indefinite Kaehler statistical manifold, Malaya Journal of Matematik, 8(2020), no. 4, 1346-1353.
  • [16] Kilic, E. and Bahadir, O.: Lightlike Hypersurfaces of a Semi-Riemannian Product Manifold and Quarter- Symmetric Nonmetric Connections, International Journal of Mathematics and Mathematical Sciences, Volume 2012, Article ID 178390, 17 pages.
  • [17] Milijevic, M.: CR-submanifolds in holomorphic statistical manifolds, Ph.D Thesis in Science, Department of Mathematics Graduates School of Science, Hokkaido University, 2015.
  • [18] Rani, V. and Kaur, J.: Cauchy Riemann-lightlike submanifolds in the aspect of an indefinite Kaehler statistical manifold, Malaya Journal of Matematik, 9(2021), no. 1, 136-143.
  • [19] Rani, V. and Kaur, J.: On structure of lightlike hypersurfaces of an indefinite Kaehler statistical manifold, Differential Geometry-Dynamical Systems, 23 (2021), 221-234.
  • [20] Rao, C.R.: Information and the accuracy attainable in the estimation of statistical parameters, Bulletin of Calcutta Mathematical Society, 37 (1945), 81-91.
  • [21] Sahin, B. and Gunes, R.: Geodesic CR-lightlike submanifolds, Beitrage zur Algebra und Geometrie, Contribution to Algebra and Geometry, 42 (2001), no.2, 583-594.
  • [22] Sahin, B.: Transversal lightlike submanifolds of indefinite Kaehler manifolds, An. Univ. Vest Timis. Ser. Mat.-Inform, 44 (2006),119-145.
  • [23] Sahin, B.: Screen transversal lightlike submanifolds of Kaehler manifolds, Chaos, Solitons and Fractals, 38 (2008),1439-1448.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Vandana Rani 0000-0003-2190-0174

Jasleen Kaur 0000-0002-4284-2842

Early Pub Date July 23, 2022
Publication Date October 31, 2022
Acceptance Date September 9, 2022
Published in Issue Year 2022 Volume: 15 Issue: 2

Cite

APA Rani, V., & Kaur, J. (2022). STCR-Lightlike Product Manifolds of an Indefinite Kaehler Statistical Manifold with a Quarter Symmetric Non-Metric Connection. International Electronic Journal of Geometry, 15(2), 229-241. https://doi.org/10.36890/iejg.1130240
AMA Rani V, Kaur J. STCR-Lightlike Product Manifolds of an Indefinite Kaehler Statistical Manifold with a Quarter Symmetric Non-Metric Connection. Int. Electron. J. Geom. October 2022;15(2):229-241. doi:10.36890/iejg.1130240
Chicago Rani, Vandana, and Jasleen Kaur. “STCR-Lightlike Product Manifolds of an Indefinite Kaehler Statistical Manifold With a Quarter Symmetric Non-Metric Connection”. International Electronic Journal of Geometry 15, no. 2 (October 2022): 229-41. https://doi.org/10.36890/iejg.1130240.
EndNote Rani V, Kaur J (October 1, 2022) STCR-Lightlike Product Manifolds of an Indefinite Kaehler Statistical Manifold with a Quarter Symmetric Non-Metric Connection. International Electronic Journal of Geometry 15 2 229–241.
IEEE V. Rani and J. Kaur, “STCR-Lightlike Product Manifolds of an Indefinite Kaehler Statistical Manifold with a Quarter Symmetric Non-Metric Connection”, Int. Electron. J. Geom., vol. 15, no. 2, pp. 229–241, 2022, doi: 10.36890/iejg.1130240.
ISNAD Rani, Vandana - Kaur, Jasleen. “STCR-Lightlike Product Manifolds of an Indefinite Kaehler Statistical Manifold With a Quarter Symmetric Non-Metric Connection”. International Electronic Journal of Geometry 15/2 (October 2022), 229-241. https://doi.org/10.36890/iejg.1130240.
JAMA Rani V, Kaur J. STCR-Lightlike Product Manifolds of an Indefinite Kaehler Statistical Manifold with a Quarter Symmetric Non-Metric Connection. Int. Electron. J. Geom. 2022;15:229–241.
MLA Rani, Vandana and Jasleen Kaur. “STCR-Lightlike Product Manifolds of an Indefinite Kaehler Statistical Manifold With a Quarter Symmetric Non-Metric Connection”. International Electronic Journal of Geometry, vol. 15, no. 2, 2022, pp. 229-41, doi:10.36890/iejg.1130240.
Vancouver Rani V, Kaur J. STCR-Lightlike Product Manifolds of an Indefinite Kaehler Statistical Manifold with a Quarter Symmetric Non-Metric Connection. Int. Electron. J. Geom. 2022;15(2):229-41.
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