Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature

Curvature Invariants for Statistical Submanifolds of Hessian Manifolds of Constant Hessian Curvature

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.

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Veröffentlicht in:Mathematics (Basel) 2018-03, Vol.6 (3), p.44
Hauptverfasser: Mihai, Adela, Mihai, Ion
Format: Artikel
Sprache:eng
Schlagworte:
Curvature
Hessian manifolds
Hessian sectional curvature
Manifolds (mathematics)
Ricci curvature
scalar curvature
statistical manifolds
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Zusammenfassung: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math6030044