On Ricci Curvature Pinching of Lagrangian Submanifolds in the Homogeneous Nearly Kähler $$\pmb {\mathbb {S}}^6(1)$$

2020 ◽  
Vol 75 (2) ◽  
Author(s):  
Zejun Hu ◽  
Zeke Yao ◽  
Jiabin Yin
Keyword(s):  
Ricci Curvature ◽  
Lagrangian Submanifolds ◽  
Nearly Kähler ◽  
Curvature Pinching

scholarly journals Upper bounds for Ricci curvatures for submanifolds in Bochner-Kaehler manifolds

2020 ◽  
Vol 51 (1) ◽  
Author(s):  
Mehraj Ahmad Lone ◽  
Yoshio Matsuyama ◽  
Falleh R. Al-Solamy ◽  
Mohammad Hasan Shahid ◽  
Mohammed Jamali
Keyword(s):  
Ricci Curvature ◽  
Riemannian Space ◽  
Space Form ◽  
Lagrangian Submanifolds ◽  
Upper Bounds ◽  
Kaehler Manifolds ◽  
Slant Submanifolds ◽  
Arbitrary Codimension ◽  
The Relationship ◽  
Algebraic Technique

Chen established the relationship between the Ricci curvature and the squared norm of meancurvature vector for submanifolds of Riemannian space form with arbitrary codimension knownas Chen-Ricci inequality. Deng improved the inequality for Lagrangian submanifolds in complexspace form by using algebraic technique. In this paper, we establish the same inequalitiesfor different submanifolds of Bochner-Kaehler manifolds. Moreover, we obtain improvedChen-Ricci inequality for Kaehlerian slant submanifolds of Bochner-Kaehler manifolds.

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