On submanifolds of Sasakian statistical manifolds
DOI:
https://doi.org/10.5269/bspm.42402Abstract
‎In this paper‎, ‎invariant and‎ ‎anti-invariant submanifolds of Sasakian statistical manifolds are studied‎. ‎Necessary and sufficient conditions are given for vanishing the dual connection in the normal bundle‎. ‎Moreover‎, ‎existence of a Kaehlerian structure on invariant hypersurfaces of Sasakian statistical manifolds are proved‎.
References
1. Amari, S. and Nagaoka, H., Methods of information geometry. Transl. Math. Monogr. 191., Amer. Math. Soc. (2000).
2. Aydin, M.E., Mihai, A. and Mihai, I., Generalized Wintgen inequality for statistical submanifolds in statistical manifolds of constant curvature. Bull. Math. Sci. 7, 155—166, (2017).
3. Furuhata, H., Hypersurfaces in statistical manifolds. Diff. Geom. Appl. 27, 420–429, (2009).
4. Furuhata, H., Hasegawa, I., Okuyama, Y., Sato, K. and Shahid, M. Sasakian statistical manifolds. J. Geom. Phys. 117, 179–186, (2017).
5. Majhi, P and Ghosh G., Certain results on generalized (k, μ)-contact manifolds. Bol. Soc. Paran. Mat. 37, 131–142, (2019).
6. Vos, P. W., Fundamental equations for statistical submanifolds with applications to the Bartlett correction. Ann. Inst. Statist. Math. 41, 429–450, (1989).
7. Yano, K. and Kon, M., Structures on manifolds. World Scientific, (1984).
2. Aydin, M.E., Mihai, A. and Mihai, I., Generalized Wintgen inequality for statistical submanifolds in statistical manifolds of constant curvature. Bull. Math. Sci. 7, 155—166, (2017).
3. Furuhata, H., Hypersurfaces in statistical manifolds. Diff. Geom. Appl. 27, 420–429, (2009).
4. Furuhata, H., Hasegawa, I., Okuyama, Y., Sato, K. and Shahid, M. Sasakian statistical manifolds. J. Geom. Phys. 117, 179–186, (2017).
5. Majhi, P and Ghosh G., Certain results on generalized (k, μ)-contact manifolds. Bol. Soc. Paran. Mat. 37, 131–142, (2019).
6. Vos, P. W., Fundamental equations for statistical submanifolds with applications to the Bartlett correction. Ann. Inst. Statist. Math. 41, 429–450, (1989).
7. Yano, K. and Kon, M., Structures on manifolds. World Scientific, (1984).
Downloads
Published
2021-12-16
Issue
Section
Research Articles
License
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
