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

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 164
Author(s):  
Adela Mihai ◽  
Ion Mihai
Keyword(s):  
Chen Inequality

We establish Chen inequality for the invariant δ ( 2 , 2 ) on statistical submanifolds in Hessian manifolds of constant Hessian curvature. Recently, in co-operation with Chen, we proved a Chen first inequality for such submanifolds. The present authors previously initiated the investigation of statistical submanifolds in Hessian manifolds of constant Hessian curvature; this paper represents a development in this topic.

Chen inequalities on lightlike hypersurfaces of a GRW spacetime

2021 ◽  
Author(s):  
Nergi̇z (Önen) Poyraz
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Lightlike Hypersurfaces ◽  
Chen Inequality

In this paper, we introduce [Formula: see text]-Ricci curvature and [Formula: see text]-scalar curvature on lightlike hypersurfaces of a GRW spacetime. Using these curvatures, we establish some inequalities for lightlike hypersurfaces of a GRW spacetime. Using these inequalities, we obtain some characterizations on lightlike hypersurfaces. We also get Chen–Ricci inequality and Chen inequality on a screen homothetic lightlike hypersurfaces of a GRW spacetime.

scholarly journals A New Algebraic Inequality and Some Applications in Submanifold Theory

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1175
Author(s):  
Ion Mihai ◽  
Radu-Ioan Mihai
Keyword(s):  
Simple Proof ◽  
Riemannian Space ◽  
Space Forms ◽  
Riemannian Space Forms ◽  
Chen Inequality

We give a simple proof of the Chen inequality involving the Chen invariant δ(k) of submanifolds in Riemannian space forms. We derive Chen’s first inequality and the Chen–Ricci inequality. Additionally, we establish a corresponding inequality for statistical submanifolds.

scholarly journals Chen Inequalities for Statistical Submanifolds of Kähler-Like Statistical Manifolds

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1202 ◽  
Author(s):  
Hülya Aytimur ◽  
Mayuko Kon ◽  
Adela Mihai ◽  
Cihan Özgür ◽  
Kazuhiko Takano
Keyword(s):  
Curvature Tensor ◽  
Natural Condition ◽  
Tensor Field ◽  
Statistical Manifolds ◽  
Chen Inequality

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 ) .

scholarly journals Improved Chen inequality of Sasakian space forms with the Tanaka-Webster connection

Filomat ◽  
2015 ◽  
Vol 29 (7) ◽  
pp. 1525-1533 ◽  
Author(s):  
Chul Lee ◽  
Jae Lee ◽  
Dae Yoon
Keyword(s):  
Ricci Curvature ◽  
Mean Curvature ◽  
Space Forms ◽  
Equality Case ◽  
Sasakian Space Forms ◽  
Invariant Submanifolds ◽  
Chen Inequality

In this paper, we establish an improved Chen inequality between the pseudo-Ricci curvature and the square of pseudo mean curvature with respect to the Tanaka-Webster connection in Sasakian space forms, and also we study an improved Chen inequality for anti-invariant submanifolds. The equality case is considered.

Some inequalities for statistical submanifolds of quaternion Kaehler-like statistical space forms

2019 ◽  
Vol 16 (08) ◽  
pp. 1950129 ◽  
Author(s):  
Mohd. Aquib
Keyword(s):  
Space Forms ◽  
Statistical Manifolds ◽  
Statistical Submanifold ◽  
Totally Real ◽  
Statistical Version ◽  
Chen Inequality ◽  
Statistical Space

Motivated by one of the problems proposed by [Vilcu and Vilcu, Statistical manifolds with almost quaternionic structures and quaternionic Kaehler-like statistical submersions, Entropy 17 (2015) 6213–6228] in this paper, we study the statistical submanifolds of quaternion Kaehler-like statistical space forms and provide an answer to the problem. Further, we derive the statistical version of Chen inequality for totally real statistical submanifold in such ambient.

scholarly journals Relations between Extrinsic and Intrinsic Invariants of Statistical Submanifolds in Sasaki-Like Statistical Manifolds

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1285
Author(s):  
Hülya Aytimur ◽  
Adela Mihai ◽  
Cihan Özgür
Keyword(s):  
Curvature Condition ◽  
Statistical Manifolds ◽  
Chen Inequality

The Chen first inequality and a Chen inequality for the δ(2,2)-invariant on statistical submanifolds of Sasaki-like statistical manifolds, under a curvature condition, are obtained.

Geometry of Chen invariants in statistical warped product manifolds

2020 ◽  
Vol 17 (06) ◽  
pp. 2050081
Author(s):  
Falleh R. Al-Solamy ◽  
Pooja Bansal ◽  
Bang-Yen Chen ◽  
Cengizhan Murathan ◽  
Mohammad Hasan Shahid
Keyword(s):  
Hyperbolic Space ◽  
Warped Product ◽  
Product Manifold ◽  
Warped Product Manifold ◽  
Statistical Submanifold ◽  
Chen Inequality

In this paper, we derive Chen inequality for statistical submanifold of statistical warped product manifolds [Formula: see text]. Further, we derive Chen inequality for Legendrian statistical submanifold in statistical warped product manifolds [Formula: see text]. We also provide some applications of derived inequalities in a statistical warped product manifold which is equivalent to a hyperbolic space. Moreover, we construct new examples of statistical warped product manifolds to support results.

scholarly journals Submanifolds in Normal Complex Contact Manifolds

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1195
Author(s):  
Adela Mihai ◽  
Ion Mihai
Keyword(s):  
Present Article ◽  
Space Form ◽  
Real Submanifolds ◽  
Maximum Dimension ◽  
Contact Manifolds ◽  
Basic Properties ◽  
Normal Complex ◽  
Contact Metric Manifolds ◽  
Totally Real ◽  
Chen Inequality

In the present article we initiate the study of submanifolds in normal complex contact metric manifolds. We define invariant and anti-invariant ( C C -totally real) submanifolds in such manifolds and start the study of their basic properties. Also, we establish the Chen first inequality and Chen inequality for the invariant δ ( 2 , 2 ) for C C -totally real submanifolds in a normal complex contact space form and characterize the equality cases. We also prove the minimality of C C -totally real submanifolds of maximum dimension satisfying the equalities.

scholarly journals An Algebraic Inequality with Applications to Certain Chen Inequalities

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 7
Author(s):  
Ion Mihai ◽  
Radu-Ioan Mihai
Keyword(s):  
Simple Proof ◽  
Riemannian Space ◽  
Space Forms ◽  
Riemannian Space Forms ◽  
Chen Inequality

We give a simple proof of the Chen inequality for the Chen invariant δ(2,⋯,2)︸kterms of submanifolds in Riemannian space forms.

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