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Screen Semi-Invariant Lightlike Hypersurfaces on Hermite-Like Manifolds

Year 2023, Issue: 45, 83 - 94, 31.12.2023

Ömer Aksu Mehmet Gülbahar

https://doi.org/10.53570/jnt.1381549

Abstract

Hermite-like manifolds, which admit two different, almost complex structures, can be considered a general concept of Hermitian manifolds. Factoring in the effects of these two complex structures on the radical, screen, and transversal spaces, a new classification of lightlike hypersurfaces of Hermite-like manifolds is proposed in the present paper. Moreover, an example of screen semi-invariant lightlike hypersurfaces of Hermite-like manifolds is provided. Besides, some results on these hypersurfaces admitting a statistical structure are obtained. Further, screen semi-invariant lightlike hypersurfaces are investigated on Kaehler-like statistical manifolds. In addition, several characteristics of totally geodesic, mixed geodesic, and totally umbilical screen lightlike hypersurfaces are obtained. Finally, the need for further research is discussed.

Keywords

Hermite-like manifolds complex structures lightlike hypersurfaces

Project Number

This work was supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) with project number 122F326.

References

  • K. Takano, Statistical Manifolds with Almost Contact Structures and Its Statistical Submersions, Journal of Geometry 85 (1-2) (2006) 171--187.
  • K. Takano, Statistical Manifolds with Almost Complex Structures, in: H. Shimada (Ed.), Proceedings of the 45th Symposium on Finsler Geometry, Tokyo, 2011, pp. 54--57.
  • M. Aquib, Some Inequalities for Statistical Submanifolds of Quaternion Kaehler-like Statistical Space Forms, International Journal of Geometric Methods in Modern Physics 16 (08) (2019) 1950129 16 pages.
  • M. Aquib, M. H. Shahid, Generalized Normalized $\delta$-Casorati Curvature for Statistical Submanifolds in Quaternion Kaehler-like Statistical Space Forms, Journal of Geometry 109 (1) (2018) Article Number 13 13 pages.
  • H. Aytimur, M. Kon, A. Mihai, C. \"{O}zg\"{u}r, K. Takano, Chen Inequalities for Statistical Submanifolds of K\"{a}hler-like Statistical Manifolds, Mathematics 7 (12) (2019) Article ID 1202 19 pages.
  • H. Aytimur, C. \"{O}zg\"{u}r, On Cosymplectic-like Statistical Submersions, Mediterranean Journal of Mathematics 16 (2019) 1--14.
  • S. Kazan, K. Takano, Anti-invariant Holomorphic Statistical Submersions, Results in Mathematics 78 (4) (2023) Article Number 128 18 pages.
  • S. Kazan, Anti-Invariant $\xi^{\bot}$-Cosymplectic-like Statistical Submersions, Thermal Science 26 (4) (2022) 2991--3001.
  • A. N. Siddiqui, S. Uddin, M. H. Shahid, B.-Y. Chen's Inequality for K\"{a}hler-like Statistical Submersions, International Electronic Journal of Geometry 15 (2) (2022) 277--286.
  • M. D. Siddiqi, A. N. Siddiqui, F. Mofarreh, H. Aytimur, A Study of Kenmotsu-like Statistical Submersions, Symmetry 14 (8) (2022) Article ID 1681 13 pages.
  • A. D. Vilcu, G. E. Vilcu, Statistical Manifolds with Almost Quaternionic Structures and Quaternionic K\"{a}hler-like Statistical Submersions, Entropy 17 (9) (2015) 6213--6228.
  • K. L. Duggal, B. \c{S}ahin, Differential Geometry of Lightlike Submanifolds, Birkhäuser, Basel, 2011.
  • K. L. Duggal, D. H. Jin, Totally Umbilical Lightlike Submanifolds, Kodai Mathematical Journal 26 (2003) 49--68.
  • S. Amari, Differential-Geometrical Methods in Statistics, Springer, New York, 1985.
  • H. Furuhata, Hypersurfaces in Statistical Manifolds, Differential Geometry and its Applications 27 (3) (2009) 420--429.
  • O. Bahad{\i}r, On Lightlike Geometry of Indefinite Sasakian Statistical Manifolds, AIMS Mathematics 6 (11) (2021) 12845--12862.
  • O. Bahad{\i}r, M. M. Tripathi, Geometry of Lightlike Hypersurfaces of a Statistical Manifold, WSEAS Transactions on Mathematics 22 (2023) 466--474.
  • O. Bahad{\i}r, A. N. Siddiqui, M. G\"{u}lbahar, A. H. Alkhaldi, Main Curvatures Identities on Lightlike Hypersurfaces of Statistical Manifolds and Their Characterizations, Mathematics 10 (13) (2022) Article ID 2290 18 pages.
  • B. E. Acet, S. Yüksel Perktaş, E. Kılı\c{c}, On Lightlike Geometry of Para-Sasakian Manifolds, The Scientific World Journal 2014 (2014) Article ID 696231 12 pages.
  • B. E. Acet, Lightlike Hypersurfaces of Metallic Semi-Riemannian Manifolds, International Journal of Geometric Methods in Modern Physics 15 (12) (2018) Article ID 1850201 16 pages.
  • E. K{\i}l{\i}\c{c}, B. \c{S}ahin, S. Kele\c{s}, Screen Semi Invariant Lightlike Submanifolds of Semi-Riemannian Product Manifolds, International Electronic Journal of Geometry 4 (2) (2011) 120--135.
  • S: Y. Perkta\c{s}, E. K{\i}l{\i}\c{c}, B. E. Acet, Lightlike Hypersurfaces of a Para-Sasakian Space Form, Gulf Journal of Mathematics 2 (2) (2014) 7--18.
  • N. \"{O}. Poyraz, E. Ya\c{s}ar, Lightlike Hypersurfaces of a Golden Semi-Riemannian Manifold, Mediterranean Journal of Mathematics 14 (2017) 1--20.
  • N. \"{O}. Poyraz, Screen Semi-Invariant Lightlike Submanifolds of Golden Semi-Riemannian Manifolds, International Electronic Journal of Geometry 14 (1) (2021) 207--216.
  • K. Yano, On the Torse-Forming Directions in Riemannian Spaces, Proceedings of the Imperial Academy Tokyo 20 (6) (1944) 340--345.

Year 2023, Issue: 45, 83 - 94, 31.12.2023

Ömer Aksu Mehmet Gülbahar

https://doi.org/10.53570/jnt.1381549

Abstract

Project Number

This work was supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) with project number 122F326.

References

  • K. Takano, Statistical Manifolds with Almost Contact Structures and Its Statistical Submersions, Journal of Geometry 85 (1-2) (2006) 171--187.
  • K. Takano, Statistical Manifolds with Almost Complex Structures, in: H. Shimada (Ed.), Proceedings of the 45th Symposium on Finsler Geometry, Tokyo, 2011, pp. 54--57.
  • M. Aquib, Some Inequalities for Statistical Submanifolds of Quaternion Kaehler-like Statistical Space Forms, International Journal of Geometric Methods in Modern Physics 16 (08) (2019) 1950129 16 pages.
  • M. Aquib, M. H. Shahid, Generalized Normalized $\delta$-Casorati Curvature for Statistical Submanifolds in Quaternion Kaehler-like Statistical Space Forms, Journal of Geometry 109 (1) (2018) Article Number 13 13 pages.
  • H. Aytimur, M. Kon, A. Mihai, C. \"{O}zg\"{u}r, K. Takano, Chen Inequalities for Statistical Submanifolds of K\"{a}hler-like Statistical Manifolds, Mathematics 7 (12) (2019) Article ID 1202 19 pages.
  • H. Aytimur, C. \"{O}zg\"{u}r, On Cosymplectic-like Statistical Submersions, Mediterranean Journal of Mathematics 16 (2019) 1--14.
  • S. Kazan, K. Takano, Anti-invariant Holomorphic Statistical Submersions, Results in Mathematics 78 (4) (2023) Article Number 128 18 pages.
  • S. Kazan, Anti-Invariant $\xi^{\bot}$-Cosymplectic-like Statistical Submersions, Thermal Science 26 (4) (2022) 2991--3001.
  • A. N. Siddiqui, S. Uddin, M. H. Shahid, B.-Y. Chen's Inequality for K\"{a}hler-like Statistical Submersions, International Electronic Journal of Geometry 15 (2) (2022) 277--286.
  • M. D. Siddiqi, A. N. Siddiqui, F. Mofarreh, H. Aytimur, A Study of Kenmotsu-like Statistical Submersions, Symmetry 14 (8) (2022) Article ID 1681 13 pages.
  • A. D. Vilcu, G. E. Vilcu, Statistical Manifolds with Almost Quaternionic Structures and Quaternionic K\"{a}hler-like Statistical Submersions, Entropy 17 (9) (2015) 6213--6228.
  • K. L. Duggal, B. \c{S}ahin, Differential Geometry of Lightlike Submanifolds, Birkhäuser, Basel, 2011.
  • K. L. Duggal, D. H. Jin, Totally Umbilical Lightlike Submanifolds, Kodai Mathematical Journal 26 (2003) 49--68.
  • S. Amari, Differential-Geometrical Methods in Statistics, Springer, New York, 1985.
  • H. Furuhata, Hypersurfaces in Statistical Manifolds, Differential Geometry and its Applications 27 (3) (2009) 420--429.
  • O. Bahad{\i}r, On Lightlike Geometry of Indefinite Sasakian Statistical Manifolds, AIMS Mathematics 6 (11) (2021) 12845--12862.
  • O. Bahad{\i}r, M. M. Tripathi, Geometry of Lightlike Hypersurfaces of a Statistical Manifold, WSEAS Transactions on Mathematics 22 (2023) 466--474.
  • O. Bahad{\i}r, A. N. Siddiqui, M. G\"{u}lbahar, A. H. Alkhaldi, Main Curvatures Identities on Lightlike Hypersurfaces of Statistical Manifolds and Their Characterizations, Mathematics 10 (13) (2022) Article ID 2290 18 pages.
  • B. E. Acet, S. Yüksel Perktaş, E. Kılı\c{c}, On Lightlike Geometry of Para-Sasakian Manifolds, The Scientific World Journal 2014 (2014) Article ID 696231 12 pages.
  • B. E. Acet, Lightlike Hypersurfaces of Metallic Semi-Riemannian Manifolds, International Journal of Geometric Methods in Modern Physics 15 (12) (2018) Article ID 1850201 16 pages.
  • E. K{\i}l{\i}\c{c}, B. \c{S}ahin, S. Kele\c{s}, Screen Semi Invariant Lightlike Submanifolds of Semi-Riemannian Product Manifolds, International Electronic Journal of Geometry 4 (2) (2011) 120--135.
  • S: Y. Perkta\c{s}, E. K{\i}l{\i}\c{c}, B. E. Acet, Lightlike Hypersurfaces of a Para-Sasakian Space Form, Gulf Journal of Mathematics 2 (2) (2014) 7--18.
  • N. \"{O}. Poyraz, E. Ya\c{s}ar, Lightlike Hypersurfaces of a Golden Semi-Riemannian Manifold, Mediterranean Journal of Mathematics 14 (2017) 1--20.
  • N. \"{O}. Poyraz, Screen Semi-Invariant Lightlike Submanifolds of Golden Semi-Riemannian Manifolds, International Electronic Journal of Geometry 14 (1) (2021) 207--216.
  • K. Yano, On the Torse-Forming Directions in Riemannian Spaces, Proceedings of the Imperial Academy Tokyo 20 (6) (1944) 340--345.
There are 25 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

Ömer Aksu This is me 0009-0003-6473-5145

Mehmet Gülbahar 0000-0001-6950-7633

Project Number This work was supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) with project number 122F326.
Early Pub Date December 30, 2023
Publication Date December 31, 2023
Submission Date October 26, 2023
Acceptance Date December 25, 2023
Published in Issue Year 2023 Issue: 45

Cite

APA Aksu, Ö., & Gülbahar, M. (2023). Screen Semi-Invariant Lightlike Hypersurfaces on Hermite-Like Manifolds. Journal of New Theory(45), 83-94. https://doi.org/10.53570/jnt.1381549
AMA Aksu Ö, Gülbahar M. Screen Semi-Invariant Lightlike Hypersurfaces on Hermite-Like Manifolds. JNT. December 2023;(45):83-94. doi:10.53570/jnt.1381549
Chicago Aksu, Ömer, and Mehmet Gülbahar. “Screen Semi-Invariant Lightlike Hypersurfaces on Hermite-Like Manifolds”. Journal of New Theory, no. 45 (December 2023): 83-94. https://doi.org/10.53570/jnt.1381549.
EndNote Aksu Ö, Gülbahar M (December 1, 2023) Screen Semi-Invariant Lightlike Hypersurfaces on Hermite-Like Manifolds. Journal of New Theory 45 83–94.
IEEE Ö. Aksu and M. Gülbahar, “Screen Semi-Invariant Lightlike Hypersurfaces on Hermite-Like Manifolds”, JNT, no. 45, pp. 83–94, December 2023, doi: 10.53570/jnt.1381549.
ISNAD Aksu, Ömer - Gülbahar, Mehmet. “Screen Semi-Invariant Lightlike Hypersurfaces on Hermite-Like Manifolds”. Journal of New Theory 45 (December 2023), 83-94. https://doi.org/10.53570/jnt.1381549.
JAMA Aksu Ö, Gülbahar M. Screen Semi-Invariant Lightlike Hypersurfaces on Hermite-Like Manifolds. JNT. 2023;:83–94.
MLA Aksu, Ömer and Mehmet Gülbahar. “Screen Semi-Invariant Lightlike Hypersurfaces on Hermite-Like Manifolds”. Journal of New Theory, no. 45, 2023, pp. 83-94, doi:10.53570/jnt.1381549.
Vancouver Aksu Ö, Gülbahar M. Screen Semi-Invariant Lightlike Hypersurfaces on Hermite-Like Manifolds. JNT. 2023(45):83-94.
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