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.

scholarly journals Ricci curvature of submanifolds in Sasakian space forms

2002 ◽  
Vol 72 (2) ◽  
pp. 247-256 ◽  
Author(s):  
Ion Mihai
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Complex Space ◽  
Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Arbitrary Codimension ◽  
Complex Space Forms

AbstractRecently, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Afterwards, we dealt with similar problems for submanifolds in complex space forms.In the present paper, we obtain sharp inequalities between the Ricci curvature and the squared mean curvature for submanifolds in Sasakian space forms. Also, estimates of the scalar curvature and the k-Ricci curvature respectively, in terms of the squared mean curvature, are proved.

scholarly journals Ricci curvature of submanifolds in Kenmotsu space forms

2002 ◽  
Vol 29 (12) ◽  
pp. 719-726 ◽  
Author(s):  
Kadri Arslan ◽  
Ridvan Ezentas ◽  
Ion Mihai ◽  
Cengizhan Murathan ◽  
Cihan Özgür
Keyword(s):  
Ricci Curvature ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Complex Space ◽  
Space Form ◽  
Space Forms ◽  
Arbitrary Codimension ◽  
Complex Space Forms

In 1999, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Similar problems for submanifolds in complex space forms were studied by Matsumoto et al. In this paper, we obtain sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in Kenmotsu space forms.

scholarly journals Ricci Curvature Inequalities for Skew CR-Warped Product Submanifolds in Complex Space Forms

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1317
Author(s):  
Meraj Ali Khan ◽  
Ibrahim Aldayel
Keyword(s):  
Ricci Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Complex Space ◽  
Space Form ◽  
Curvature Vector ◽  
Mean Curvature Vector ◽  
Space Forms ◽  
Fundamental Goal ◽  
Complex Space Forms

The fundamental goal of this study was to achieve the Ricci curvature inequalities for a skew CR-warped product (SCR W-P) submanifold isometrically immersed in a complex space form (CSF) in the expressions of the squared norm of mean curvature vector and warping functions (W-F). The equality cases were likewise examined. In particular, we also derived Ricci curvature inequalities for CR-warped product (CR W-P) submanifolds. To sustain this study, an example of these submanifolds is provided.

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.

scholarly journals C-totally real submanifolds in (κ,μ)-contact space forms

2003 ◽  
Vol 67 (1) ◽  
pp. 51-65 ◽  
Author(s):  
Mukut Mani Tripathi ◽  
Jeong-Sik Kim
Keyword(s):  
Ricci Curvature ◽  
Mean Curvature ◽  
Space Form ◽  
Real Submanifolds ◽  
Space Forms ◽  
Left Hand ◽  
Real Submanifold ◽  
The Right ◽  
Totally Real ◽  
Contact Space

We obtain a basic B,-Y. Chen's inequality for a C-totally real submanifold in a (κ,μ)-contact space form involving intrinsic invariants, namely the scalar curvature and the sectional curvatures of the submanifold on left hand side and the main extrinsic invariant, namely the squared mean curvature on the right hand side. Inequalities between the squared mean curvature and Ricci curvature and between the squared mean curvature and κ-Ricci curvature are also obtained. These results are applied to get corresponding results for C-totally real submanifolds in a Sasakian space form.

Ricci curvature on warped product submanifolds of complex space forms and its applications

2019 ◽  
Vol 16 (09) ◽  
pp. 1950142 ◽  
Author(s):  
Akram Ali ◽  
Pişcoran Laurian-Ioan ◽  
Ali H. Alkhaldi ◽  
Lamia Saeed Alqahtani
Keyword(s):  
Ricci Curvature ◽  
Warped Product ◽  
Complex Space ◽  
Shape Operator ◽  
Isometric Immersions ◽  
Differential Function ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Arbitrary Codimension ◽  
Complex Space Forms

The upper bound of Ricci curvature conjecture, also known as Chen-Ricci conjecture, was formulated by Chen [B. Y. Chen, Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimension, Glasgow Math. J. 41 (1999) 33–41] and modified by Tripathi [M. M. Tripathi, Improved Chen–Ricci inequality for curvature-like tensors and its applications, Diff. Geom. Appl. 29 (2011) 685–698]. In this paper, first, we define partially minimal isometric immersion of warped product manifolds. Then, we derive a fundamental theorem for Ricci curvature via partially minimal isometric immersions from a warped product pointwise bi-slant submanifolds into complex space forms. Some applications are constructed in terms of Dirichlet energy function, Hamiltonian, Lagrangian and Hessian tensor due to appearance of the positive differential function in the inequality.

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 The First Fundamental Equation and Generalized Wintgen-Type Inequalities for Submanifolds in Generalized Space Forms

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1151 ◽  
Author(s):  
Mohd. Aquib ◽  
Michel Nguiffo Boyom ◽  
Mohammad Hasan Shahid ◽  
Gabriel-Eduard Vîlcu
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Fundamental Equation ◽  
Type Inequality ◽  
Lagrangian Submanifold ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Sasakian Space Forms ◽  
Generalized Complex ◽  
Complex Space Forms

In this work, we first derive a generalized Wintgen type inequality for a Lagrangian submanifold in a generalized complex space form. Further, we extend this inequality to the case of bi-slant submanifolds in generalized complex and generalized Sasakian space forms and derive some applications in various slant cases. Finally, we obtain obstructions to the existence of non-flat generalized complex space forms and non-flat generalized Sasakian space forms in terms of dimension of the vector space of solutions to the first fundamental equation on such spaces.

scholarly journals Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions

1999 ◽  
Vol 41 (1) ◽  
pp. 33-41 ◽  
Author(s):  
BANG-YEN CHEN
Keyword(s):  
Ricci Curvature ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Space Form ◽  
Shape Operator ◽  
Arbitrary Codimension

First we define the notion of k-Ricci curvature of a Riemannian n-manifold. Then we establish sharp relations between the k-Ricci curvature and the shape operator and also between the k-Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. Several applications of such relationships are also presented.

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