Screen Semi-Invariant Lightlike Hypersurfaces on Hermite-Like Manifolds
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.