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Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature
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Inequalities for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

Aliya Naaz Siddiqui, Kamran Ahmad and Cenap Özel
Geometric Science of Information, pp.389-397
Lecture Notes in Computer Science, Springer International Publishing
02/08/2019
DOI: https://doi.org/10.1007/978-3-030-26980-7_40

Abstract

Casorati curvatures Einstein-Hessian manifolds Hessian manifolds
In the present paper, we study Hessian and Einstein-Hessian manifolds with some examples. We establish optimizations of the intrinsic invariant (normalized scalar curvature) for a new extrinsic invariant (generalized normalized Casorati curvatures) on statistical submanifolds in a Hessian manifold of constant Hessian curvature by using algebraic technique. We consider the equality case of the derived inequalities.

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