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Article

Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds

1
Department of Mathematics, Faculty of Natural Sciences, Jamia Millia Islamia, New Delhi 110025, India
2
Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824-1027, USA
3
Department of Mathematics, Faculty of Science and Letters, Kahramanmaras Sutcu Imam University, Kahrmanmaras 46100, Turkey
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(9), 797; https://doi.org/10.3390/math7090797
Received: 25 July 2019 / Revised: 25 August 2019 / Accepted: 26 August 2019 / Published: 1 September 2019
(This article belongs to the Special Issue Inequalities in Geometry and Applications)
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. View Full-Text
Keywords: statistical warped product submanifold; statistical manifold; B.Y.Chen inequality; Casorati curvatures; statistical soliton statistical warped product submanifold; statistical manifold; B.Y.Chen inequality; Casorati curvatures; statistical soliton
MDPI and ACS Style

Siddiqui, A.N.; Chen, B.-Y.; Bahadir, O. Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds. Mathematics 2019, 7, 797. https://doi.org/10.3390/math7090797

AMA Style

Siddiqui AN, Chen B-Y, Bahadir O. Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds. Mathematics. 2019; 7(9):797. https://doi.org/10.3390/math7090797

Chicago/Turabian Style

Siddiqui, Aliya N., Bang-Yen Chen, and Oguzhan Bahadir. 2019. "Statistical Solitons and Inequalities for Statistical Warped Product Submanifolds" Mathematics 7, no. 9: 797. https://doi.org/10.3390/math7090797

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