Curvature invariants of slant submanifolds in S-space forms

2021 ◽  
Author(s):  
P. Alegre ◽  
J. Barrera ◽  
A. Carriazo ◽  
L. M. Fernández
Keyword(s):  
Space Forms ◽  
Slant Submanifolds ◽  
Curvature Invariants

scholarly journals Geometric Mechanics on Warped Product Semi-Slant Submanifold of Generalized Complex Space Forms

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Yanlin Li ◽  
Ali H. Alkhaldi ◽  
Akram Ali
Keyword(s):  
Warped Product ◽  
Complex Space ◽  
Slant Submanifold ◽  
Codazzi Equation ◽  
Space Forms ◽  
Kaehler Manifolds ◽  
Slant Submanifolds ◽  
Generalized Complex ◽  
Complex Space Forms ◽  
Nearly Kaehler Manifold

In this study, we develop a general inequality for warped product semi-slant submanifolds of type M n = N T n 1 × f N ϑ n 2 in a nearly Kaehler manifold and generalized complex space forms using the Gauss equation instead of the Codazzi equation. There are several applications that can be developed from this. It is also described how to classify warped product semi-slant submanifolds that satisfy the equality cases of inequalities (determined using boundary conditions). Several results for connected, compact warped product semi-slant submanifolds of nearly Kaehler manifolds are obtained, and they are derived in the context of the Hamiltonian, Dirichlet energy function, gradient Ricci curvature, and nonzero eigenvalue of the Laplacian of the warping functions.

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.

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 Estimation of inequalities for warped product semi-slant submanifolds of Kenmotsu space forms

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Misbah Liaqat ◽  
Piscoran Laurian-Ioan ◽  
Wan Ainun Mior Othman ◽  
Akram Ali ◽  
Abdullah Gani ◽  
...  
Keyword(s):  
Warped Product ◽  
Space Forms ◽  
Slant Submanifolds

scholarly journals On the normal scalar curvature conjecture for legendrian submanifolds in Kenmotsu space forms

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 3885-3891
Author(s):  
Monia Naghi ◽  
Mica Stankovic ◽  
Fatimah Alghamdi
Keyword(s):  
Scalar Curvature ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Legendrian Submanifolds

In this paper, we prove DDVV conjecture (the generalized Wintgen inequality) for Legendrian submanifolds in Kenmotsu space forms. Further, we derive an inequality for slant submanifolds in Kenmotsu space forms.

scholarly journals Ricci tensor of slant submanifolds in complex space forms

2003 ◽  
Vol 26 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Koji Matsumoto ◽  
Ion Mihai ◽  
Yoshihiko Tazawa
Keyword(s):  
Ricci Tensor ◽  
Complex Space ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Complex Space Forms
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