Geometric inequalities for non-integrable distributions in statistical manifolds with constant curvature

He, Guangping; Zhang, Juan; Zhao, Peibiao

doi:10.2298/fil2111585h

Cited by 3 publications

(1 citation statement)

References 18 publications

(25 reference statements)

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“…In [199], P. Bansal, S. Uddin and M. H. Shahid derived a first Chen-type inequality for statistical submanifolds of a statistical manifold of a quasi-constant curvature. Also, G. He, J. Zhang and P. Zhao derived in [200] a first Chen-type inequality for a statistical submanifold of a statistical manifold M of a constant curvature, such that M admits a nonintegrable distribution on M with a constant rank.…”

Section: Inequality For Statistical Submanifolds Of Statistical Manif...mentioning

confidence: 99%

Recent Developments on the First Chen Inequality in Differential Geometry

Chen,

Vîlcu

2023

Mathematics

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One of the most fundamental interests in submanifold theory is to establish simple relationships between the main extrinsic invariants and the main intrinsic invariants of submanifolds and find their applications. In this respect, the first author established, in 1993, a basic inequality involving the first δ-invariant, δ(2), and the squared mean curvature of submanifolds in real space forms, known today as the first Chen inequality or Chen’s first inequality. Since then, there have been many papers dealing with this inequality. The purpose of this article is, thus, to present a comprehensive survey on recent developments on this inequality performed by many geometers during the last three decades.

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Section: Inequality For Statistical Submanifolds Of Statistical Manif...mentioning

confidence: 99%

Recent Developments on the First Chen Inequality in Differential Geometry

Chen,

Vîlcu

2023

Mathematics

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Recent Developments on Chen–Ricci Inequalities in Differential Geometry

Chen,

Blaga

2024

Infosys Science Foundation Series

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Quarter-Symmetric Non-Metric Connection of Non-Integrable Distributions

Chen,

Liu

2024

Symmetry

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In this paper, we focus on non-integrable distributions with a quarter-symmetric non-metric connection (QSNMC) in generalized Riemannian manifold. First, by studying a quarter-symmetric connection on the generalized Riemannian manifold, we obtain the condition that the connection is non-metric. Then, the Gauss, Codazzi and Ricci equations are proved for non-integrable distributions with respect to a quarter-symmetric non-metric connection in generalized Riemannian manifold. Furthermore, we deduce Chen’s inequalities for non-integrable distributions of real space forms with a quarter-symmetric non-metric connection in generalized Riemannian manifold as applications. After that, we give some examples of non-integrable distributions in Riemannian manifold with quarter-symmetric non-metric connection.

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Geometric inequalities for non-integrable distributions in statistical manifolds with constant curvature

Abstract: In this paper, we make Euler inequality, Chen first inequality and Chen-Ricci inequality for non-integrable distributions in statistical manifolds with constant curvatures. Moreover, we investigate the conditions for equality cases.

Cited by 3 publications

References 18 publications

Recent Developments on the First Chen Inequality in Differential Geometry

Recent Developments on the First Chen Inequality in Differential Geometry

Recent Developments on Chen–Ricci Inequalities in Differential Geometry

Quarter-Symmetric Non-Metric Connection of Non-Integrable Distributions

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