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Search Results (3)

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Keywords = Hessian sectional curvature

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10 pages, 263 KiB  
Article
Generalized Wintgen Inequality for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature
by Aliya Naaz Siddiqui, Ali Hussain Alkhaldi and Lamia Saeed Alqahtani
Mathematics 2022, 10(10), 1727; https://doi.org/10.3390/math10101727 - 18 May 2022
Cited by 5 | Viewed by 1458
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Geometry of Manifolds and Applications)
8 pages, 258 KiB  
Article
The δ(2,2)-Invariant on Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature
by Adela Mihai and Ion Mihai
Entropy 2020, 22(2), 164; https://doi.org/10.3390/e22020164 - 31 Jan 2020
Cited by 14 | Viewed by 2185
Abstract
We establish Chen inequality for the invariant δ ( 2 , 2 ) on statistical submanifolds in Hessian manifolds of constant Hessian curvature. Recently, in co-operation with Chen, we proved a Chen first inequality for such submanifolds. The present authors previously initiated the [...] Read more.
We establish Chen inequality for the invariant δ ( 2 , 2 ) on statistical submanifolds in Hessian manifolds of constant Hessian curvature. Recently, in co-operation with Chen, we proved a Chen first inequality for such submanifolds. The present authors previously initiated the investigation of statistical submanifolds in Hessian manifolds of constant Hessian curvature; this paper represents a development in this topic. Full article
(This article belongs to the Section Multidisciplinary Applications)
8 pages, 206 KiB  
Article
Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature
by Adela Mihai and Ion Mihai
Mathematics 2018, 6(3), 44; https://doi.org/10.3390/math6030044 - 15 Mar 2018
Cited by 35 | Viewed by 4686
Abstract
We consider statistical submanifolds of Hessian manifolds of constant Hessian curvature. For such submanifolds we establish a Euler inequality and a Chen-Ricci inequality with respect to a sectional curvature of the ambient Hessian manifold. Full article
(This article belongs to the Special Issue Differential Geometry)
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