The δ(2,2)-Invariant on Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

Mihai, Adela; Iordache, Mihai

doi:10.3390/e22020164

Cited by 14 publications

(5 citation statements)

References 17 publications

(27 reference statements)

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“…We need the following algebraic lemma from [24] to prove the δ(2, 2) Chen-type inequality for statistical submersions in [31].…”

Section: On Puttingmentioning

confidence: 99%

A study of statistical submersions

Siddiqui

Ahmad²

2023

Tamkang J. Math.

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In the sixties, A. Gray \cite{Gr} and B. O'Neill \cite{O1} come with the notion of Riemannian submersions as a tool to study the geometry of a Riemannian manifold with an additional structure in terms of the fibers and the base space. Riemannian submersions have long been an effective tool to construct Riemannian manifolds with positive or nonnegative sectional curvature in Riemannian geometry and compare certain manifolds within differential geometry. In particular, many examples of Einstein manifolds can be constructed by using such submersions. It is very well known that Riemannian submersions have applications in physics, for example Kaluza-Klein theory, Yang-Mills theory, supergravity and superstring theories.

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“…We need the following algebraic lemma from [24] to prove the δ(2, 2) Chen-type inequality for statistical submersions in [31].…”

Section: On Puttingmentioning

confidence: 99%

A study of statistical submersions

Siddiqui

Ahmad²

2023

Tamkang J. Math.

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“…Chen et al [10]. After that, particular cases of Chen inequalities in statistical settings were obtained (see [11][12][13][14][15][16][17][18]).…”

Section: General Chen Inequalitiesmentioning

confidence: 99%

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

Iordache

Mihai

2022

Mathematics

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Chen’s first inequality for statistical submanifolds in Hessian manifolds of constant Hessian curvature was obtained by B.-Y. Chen et al. Other particular cases of Chen inequalities in a statistical setting were given by different authors. The objective of the present article is to establish the general Chen inequalities for statistical submanifolds in Hessian manifolds of constant Hessian curvature.

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“…The following algebraic lemma from [14] has the key role in the proof of the main result of this section. Lemma 3.…”

Section: A Chen δ(2 2) Inequalitymentioning

confidence: 99%

Chen Inequalities for Statistical Submanifolds of Kähler-Like Statistical Manifolds

et al. 2019

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We consider Kähler-like statistical manifolds, whose curvature tensor field satisfies a natural condition. For their statistical submanifolds, we prove a Chen first inequality and a Chen inequality for the invariant δ(2, 2). MSC: 53C05; 53C40where ∇ 0 is the Levi-Civita connection on M.Similar definitions can be considered for semi-Riemannian manifolds (see also [5]).A statistical structure is said to be of constant curvature ∈ R [6] if:for any vector fields X, Y, Z. The same equation holds for R * (X, Y)Z.A statistical structure of null constant curvature is called a Hessian structure. In [2,7], K. Takano considered a (semi-)Riemannian manifold M, g with an almost complex structure J, endowed with another tensor field J * of type (1, 1) satisfying:for vector fields X and Y on M, g . Then, M, g, J is called an almost Hermite-like manifold. It is easy to see that J * * = J, J * 2 = −I and g JX, J * Y = g (X, Y) . If J is parallel with respect to ∇, then M, g, ∇, J is called a Kähler-like statistical manifold [7]. One also has: g

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The δ(2,2)-Invariant on Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature

Cited by 14 publications

References 17 publications

A study of statistical submersions

A study of statistical submersions

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

Chen Inequalities for Statistical Submanifolds of Kähler-Like Statistical Manifolds

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