Generalized Wintgen Inequality for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

Aliya Naaz Siddiqui, Ali Hussain Alkhaldi and Lamia Saeed Alqahtani
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Aliya Naaz Siddiqui: Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), Ambala 133207, India
Ali Hussain Alkhaldi: Department of Mathematics, College of Science, King Khalid University, Abha 9004, Saudi Arabia
Lamia Saeed Alqahtani: Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 10, issue 10, 1-10

Abstract: The geometry of Hessian manifolds is a fruitful branch of physics, statistics, Kaehlerian and affine differential geometry. The study of inequalities for statistical submanifolds in Hessian manifolds of constant Hessian curvature was truly initiated in 2018 by Mihai, A. and Mihai, I. who dealt with Chen-Ricci and Euler inequalities. Later on, Siddiqui, A.N., Ahmad K. and Ozel C. came with the study of Casorati inequality for statistical submanifolds in the same ambient space by using algebraic technique. Also, Chen, B.-Y., Mihai, A. and Mihai, I. obtained a Chen first inequality for such submanifolds. In 2020, Mihai, A. and Mihai, I. studied the Chen inequality for δ ( 2 , 2 ) -invariant. In the development of this topic, we establish the generalized Wintgen inequality for statistical submanifolds in Hessian manifolds of constant Hessian curvature. Some examples are also discussed at the end.

Keywords: statistical manifold; hessian manifold; hessian sectional curvature; generalized Wintgen inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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