Curvature invariants for statistical submanifolds of Hessian manifolds of constant Hessian curvature

DOI10.3390/math6030044zbMath1393.53046OpenAlexW2790561875WikidataQ126180361 ScholiaQ126180361MaRDI QIDQ1649116

Ion Mihai, Adela-Gabriela Mihai

Publication date: 5 July 2018

Published in: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3390/math6030044

zbMATH Keywords

scalar curvatureRicci curvatureHessian manifoldsstatistical manifoldsHessian sectional curvature

Mathematics Subject Classification ID

Global submanifolds (53C40) Connections (general theory) (53C05)

Related Items (14)

On Ricci curvature of submanifolds in statistical manifolds of constant (quasi-constant) curvature ⋮ Basic inequalities for statistical submanifolds in Golden-like statistical manifolds ⋮ On the normal scalar curvature conjecture for legendrian submanifolds in Kenmotsu space forms ⋮ Einstein statistical warped product manifolds ⋮ On the normal scalar curvature conjecture in Kenmotsu statistical manifolds ⋮ Casorati curvatures of submanifolds in cosymplectic statistical space forms ⋮ SOME PINCHING RESULTS FOR STATISTICAL SUBMANIFOLDS IN COSYMPLECTIC STATISTICAL MANIFOLDS ⋮ Inequalities for submanifolds in statistical manifolds of quasi-constant curvature ⋮ Inequalities for submanifolds of Sasaki-like statistical manifolds ⋮ A Chen first inequality for statistical submanifolds in Hessian manifolds of constant Hessian curvature ⋮ Sharp inequalities for anti-invariant Riemannian submersions from Sasakian space forms ⋮ Statistical submanifolds from a viewpoint of the Euler inequality ⋮ Statistical manifolds and their submanifolds. Results on Chen-like invariants ⋮ Curvature invariants for anti-invariant Riemannian submersions from cosymplectic space forms

Cites Work

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• A sectional curvature for statistical structures
• Generalized Wintgen inequality for statistical submanifolds in statistical manifolds of constant curvature
• Fundamental equations for statistical submanifolds with applications to the Bartlett correction
• Differential-geometrical methods in statistics
• Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions
• Mean curvature and shape operator of isometric immersions in real-space-forms
• Some inequalities on submanifolds in statistical manifolds of constant curvature

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