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 On 3-dimensional contact slant submanifolds in Sasakian space forms

2003 ◽  
Vol 68 (2) ◽  
pp. 275-283 ◽  
Author(s):  
Ion Mihai ◽  
Yoshihiko Tazawa
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Sharp Inequality ◽  
Sasakian Space Form ◽  
Slant Submanifold ◽  
Space Forms ◽  
3 Dimensional ◽  
Slant Submanifolds ◽  
Sasakian Space Forms ◽  
Complex Space Forms

Recently, B.-Y. Chen obtained an inequality for slant surfaces in complex space forms. Further, B.-Y. Chen and one of the present authors proved the non-minimality of proper slant surfaces in non-flat complex space forms. In the present paper, we investigate 3-dimensional proper contact slant submanifolds in Sasakian space forms. A sharp inequality is obtained between the scalar curvature (intrinsic invariant) and the main extrinsic invariant, namely the squared mean curvature.It is also shown that a 3-dimensional contact slant submanifold M of a Sasakian space form M̆(c), with c ≠ 1, cannot be minimal.

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.

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

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ali H. Al-Khaldi ◽  
Mohd. Aquib ◽  
Mohd Aslam ◽  
Meraj Ali Khan
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Lagrangian Submanifold ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Generalized Complex ◽  
Metric Connection ◽  
Generalized Sasakian Space Form ◽  
Symmetric Connection ◽  
Legendrian Submanifold

In this article, we obtain improved Chen-Ricci inequalities for submanifolds of generalized space forms with quarter-symmetric metric connection, with the help of which we completely characterized the Lagrangian submanifold in generalized complex space form and a Legendrian submanifold in a generalized Sasakian space form. We also discuss some geometric applications of the obtained results.

scholarly journals On generalized complex space forms satisfying certain curvature conditions

2016 ◽  
Vol 8 (2) ◽  
pp. 284-294
Author(s):  
M.M. Praveena ◽  
C.S. Bagewadi
Keyword(s):  
Scalar Curvature ◽  
Curvature Tensor ◽  
Complex Space ◽  
Space Form ◽  
Constant Scalar Curvature ◽  
Ricci Soliton ◽  
Space Forms ◽  
Generalized Complex ◽  
Curvature Tensors ◽  
Complex Space Forms

We study Ricci soliton $(g,V,\lambda)$ of generalized complex space forms when the Riemannian, Bochner and $W_{2}$ curvature tensors satisfy certain curvature conditions like semi-symmetric, Einstein semi-symmetric, Ricci pseudo symmetric and Ricci generalized pseudo symmetric. In this study it is shown that shrinking, steady and expansion of the generalized complex space forms depends on the solenoidal property of vector $V$. Also we prove that generalized complex space form with conservative Bochner curvature tensor is constant scalar curvature.

scholarly journals B.-Y. CHEN INEQUALITIES FOR SUBMANIFOLDS IN GENERALIZED COMPLEX SPACE FORMS

2003 ◽  
Vol 40 (3) ◽  
pp. 411-423 ◽  
Author(s):  
Jeong-Sik Kim ◽  
Yeong-Moo Song ◽  
Mukut-Mani Tripathi
Keyword(s):  
Complex Space ◽  
Space Forms ◽  
Generalized Complex ◽  
Complex Space Forms
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