Chen-Ricci Inequalities with a Quarter Symmetric Connection in Generalized Space Forms

Alkhaldi, Ali H.; Aquib, Mohd.; Aslam, Muhammad; Khan, Meraj Ali

doi:10.1155/2021/3221643

Cited by 3 publications

(2 citation statements)

References 24 publications

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“…Since then, this inequality has drawn attention from many geometers around the world. Consequently, a number of geometers have proven many similar inequalities for various types of submanifolds in various ambient manifolds [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Chen–Ricci Inequality for Isotropic Submanifolds in Locally Metallic Product Space Forms

Li,

Khan,

Aquib

et al. 2024

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In this article, we study isotropic submanifolds in locally metallic product space forms. Firstly, we establish the Chen–Ricci inequality for such submanifolds and determine the conditions under which the inequality becomes equality. Additionally, we explore the minimality of Lagrangian submanifolds in locally metallic product space forms, and we apply the result to create a classification theorem for isotropic submanifolds whose mean curvature is constant. More specifically, we have demonstrated that the submanifolds are either a product of two Einstein manifolds with Einstein constants, or they are isometric to a totally geodesic submanifold. To support our findings, we provide several examples.

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Section: Introductionmentioning

confidence: 99%

Chen–Ricci Inequality for Isotropic Submanifolds in Locally Metallic Product Space Forms

Li,

Khan,

Aquib

et al. 2024

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“…Sular [21] obtained Chen inequalities for submanifolds of generalized space forms with a semi-symmetric metric connection. Al-Khaldi et al [22] obtained the Chen-Ricci inequalities Lagrangian submanifold in generalized complex space form and a Legendrian submanifold in a generalized Sasakian-space-form endowed with the quarter-symmetric connection.…”

Section: Introductionmentioning

confidence: 99%

Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms

Khatri

Singh

et al. 2022

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In this article, we derive Chen’s inequalities involving Chen’s δ-invariant δM, Riemannian invariant δ(m1,⋯,mk), Ricci curvature, Riemannian invariant Θk(2≤k≤m), the scalar curvature and the squared of the mean curvature for submanifolds of generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application of the obtain inequality, we first derived the Chen inequality for the bi-slant submanifold of generalized Sasakian-space-forms.

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Recent Developments on Chen–Ricci Inequalities in Differential Geometry

Chen,

Blaga

2024

Infosys Science Foundation Series

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Chen-Ricci Inequalities with a Quarter Symmetric Connection in Generalized Space Forms

Cited by 3 publications

References 24 publications

Chen–Ricci Inequality for Isotropic Submanifolds in Locally Metallic Product Space Forms

Chen–Ricci Inequality for Isotropic Submanifolds in Locally Metallic Product Space Forms

Improved Chen’s Inequalities for Submanifolds of Generalized Sasakian-Space-Forms

Recent Developments on Chen–Ricci Inequalities in Differential Geometry

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