On Ricci curvature of isotropic and Lagrangian submanifolds in complex space forms

2000 ◽  
Vol 74 (2) ◽  
pp. 154-160 ◽  
Author(s):  
B.-Y. Chen
Keyword(s):  
Ricci Curvature ◽  
Complex Space ◽  
Lagrangian Submanifolds ◽  
Space Forms ◽  
Complex Space Forms

scholarly journals Analysis of Obata’s Differential Equations on Pointwise Semislant Warped Product Submanifolds of Complex Space Forms via Ricci Curvature

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Amira A. Ishan
Keyword(s):  
Differential Equations ◽  
Ricci Curvature ◽  
Warped Product ◽  
Complex Space ◽  
Space Forms ◽  
Geometric Conditions ◽  
Isometric To A Sphere ◽  
Complex Space Forms

The present paper studies the applications of Obata’s differential equations on the Ricci curvature of the pointwise semislant warped product submanifolds. More precisely, by analyzing Obata’s differential equations on pointwise semislant warped product submanifolds, we demonstrate that, under certain conditions, the base of these submanifolds is isometric to a sphere. We also look at the effects of certain differential equations on pointwise semislant warped product submanifolds and show that the base is isometric to a special type of warped product under some geometric conditions.

scholarly journals Certain inequalities for submanifolds in (K,μ)-contact space forms

2001 ◽  
Vol 64 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Kadri Arslan ◽  
Ridvan Ezentas ◽  
Ion Mihai ◽  
Cengizhan Murathan ◽  
Cihan Özgür
Keyword(s):  
Ricci Curvature ◽  
Mean Curvature ◽  
Complex Space ◽  
Space Form ◽  
Space Forms ◽  
Arbitrary Codimension ◽  
Complex Space Forms ◽  
Contact Space

Chen (1999) established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemanian space form with arbitrary codimension. Matsumoto (to appear) dealt with similar problems for sub-manifolds in complex space forms.In this article we obtain sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in (K, μ)-contact space forms.

Some inequalities of slant submanifolds in generalized complex space forms

2005 ◽  
Vol 36 (3) ◽  
pp. 223-229 ◽  
Author(s):  
Aimin Song ◽  
Ximin Liu
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Mean Curvature ◽  
Complex Space ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Generalized Complex ◽  
Complex Space Forms ◽  
Normalized Scalar Curvature

In this paper, we obtain an inequality about Ricci curvature and squared mean curvature of slant submanifolds in generalized complex space forms. We also obtain an inequality about the squared mean curvature and the normalized scalar curvature of slant submanifolds in generalized coplex space forms.

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