Extremities for statistical submanifolds in Kenmotsu statistical manifolds
作者： Young Jin Suh , Aliya Naaz Siddiqui , Oğuzhan Bahadır
DOI:
关键词: Statistical manifold 、 Pure mathematics 、 Manifold 、 Mathematics 、 Constant (mathematics) 、 Contact geometry 、 Curvature
摘要: Kenmotsu geometry is a valuable part of contact with nice applications in other fields such as theoretical physics. In this article, we study the statistical counterpart manifold, that is, manifold some related examples. We investigate curvature properties manifolds. prove not Ricci-flat an example. Finally, very well-known Chen-Ricci inequality for submanifolds manifolds constant $\phi-$sectional by adopting optimization techniques on submanifolds. This article ends concluding remarks.
arxiv.org参考文章(17)
Teodor Oprea, On a geometric inequality arXiv: Differential Geometry. ,(2005)
Shun-ichi Amari, Differential-geometrical methods in statistics ,(1985)
Muhittin Aydin, Adela Mihai, Ion Mihai, Some inequalities on submanifolds in statistical manifolds of constant curvature Filomat. ,vol. 29, pp. 465- 477 ,(2015) , 10.2298/FIL1503465A
Barbara Opozda, Bochner’s technique for statistical structures Annals of Global Analysis and Geometry. ,vol. 48, pp. 357- 395 ,(2015) , 10.1007/S10455-015-9475-Z
Katsuei Kenmotsu, A class of almost contact Riemannian manifolds Tohoku Mathematical Journal. ,vol. 24, pp. 93- 103 ,(1972) , 10.2748/TMJ/1178241594
Bang-Yen Chen, Some pinching and classification theorems for minimal submanifolds Archiv der Mathematik. ,vol. 60, pp. 568- 578 ,(1993) , 10.1007/BF01236084
Carlos J. G. Machado, Juan de Dios Pérez, Imsoon Jeong, Young Jin Suh, Real hypersurfaces in complex two-plane Grassmannians whose normal Jacobi operator is of Codazzi type Open Mathematics. ,vol. 9, pp. 578- 582 ,(2011) , 10.2478/S11533-011-0022-2
Bang-Yen Chen, None, Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions Glasgow Mathematical Journal. ,vol. 41, pp. 33- 41 ,(1999) , 10.1017/S0017089599970271
Paul W. Vos, FUNDAMENTAL EQUATIONS FOR STATISTICAL SUBMANIFOLDS WITH APPLICATIONS TO THE BARTLETT CORRECTION Annals of the Institute of Statistical Mathematics. ,vol. 41, pp. 429- 450 ,(1989) , 10.1007/BF00050660
Hitoshi Furuhata, Hypersurfaces in statistical manifolds Differential Geometry and its Applications. ,vol. 27, pp. 420- 429 ,(2009) , 10.1016/J.DIFGEO.2008.10.019