Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds

Aliya Naaz Siddiqui, Bang-Yen Chen and Oguzhan Bahadir
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Aliya Naaz Siddiqui: Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, India
Bang-Yen Chen: Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824-1027, USA
Oguzhan Bahadir: Department of Mathematics, Faculty of Science and Letters, Kahramanmaras Sutcu Imam University, Kahrmanmaras 46100, Turkey

Mathematics, 2019, vol. 7, issue 9, 1-19

Abstract: 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 R × f N 2 and N 1 × f 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.

Keywords: statistical warped product submanifold; statistical manifold; B.Y.Chen inequality; Casorati curvatures; statistical soliton (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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