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- Title
Generalized Wintgen Inequality for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature.
- Authors
Siddiqui, Aliya Naaz; Alkhaldi, Ali Hussain; Alqahtani, Lamia Saeed
- 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.
- Subjects
SUBMANIFOLDS; AFFINE geometry; DIFFERENTIAL geometry; CURVATURE; ALGEBRAIC spaces
- Publication
Mathematics (2227-7390), 2022, Vol 10, Issue 10, p1727
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math10101727