Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds

Mathematics

AliyaNaaz Siddiqui¹  Oguzhan Bahadir²  Bang-Yen Chen³ 

[1] Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, India;Department of Mathematics, Faculty of Science and Letters, Kahramanmaras Sutcu Imam University, Kahrmanmaras 46100, Turkey;Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824-1027, USA;

关键词: statistical warped product submanifold;    statistical manifold;    B.Y.Chen inequality;    Casorati curvatures;    statistical soliton;   

DOI  :  10.3390/math7090797

来源: DOAJ

【 摘 要 】

Warped products play crucial roles in differential geometry, as well as in mathematical physics, especially in general relativity. In this article, first we define and study statistical solitons on Ricci-symmetric statistical warped products $\mathbb{R}{\times }_{\mathfrak{f}}{N}_2$ and $N_1{\times }_{\mathfrak{f}}\mathbb{R}$ . Second, we study statistical warped products as submanifolds of statistical manifolds. For statistical warped products statistically immersed in a statistical manifold of constant curvature, we prove Chen’s inequality involving scalar curvature, the squared mean curvature, and the Laplacian of warping function (with respect to the Levi−Civita connection). At the end, we establish a relationship between the scalar curvature and the Casorati curvatures in terms of the Laplacian of the warping function for statistical warped product submanifolds in the same ambient space.

【 授权许可】

Unknown