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 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 Some Eigenvalues Estimate for the ϕ -Laplace Operator on Slant Submanifolds of Sasakian Space Forms

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yanlin Li ◽  
Akram Ali ◽  
Fatemah Mofarreh ◽  
Abimbola Abolarinwa ◽  
Rifaqat Ali
Keyword(s):  
Riemannian Manifolds ◽  
Space Form ◽  
Upper Bounds ◽  
Laplacian Operator ◽  
First Eigenvalue ◽  
Sasakian Space Form ◽  
Slant Submanifold ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Sasakian Space Forms

This paper is aimed at establishing new upper bounds for the first positive eigenvalue of the ϕ -Laplacian operator on Riemannian manifolds in terms of mean curvature and constant sectional curvature. The first eigenvalue for the ϕ -Laplacian operator on closed oriented m -dimensional slant submanifolds in a Sasakian space form M ~ 2 k + 1 ε is estimated in various ways. Several Reilly-like inequalities are generalized from our findings for Laplacian to the ϕ -Laplacian on slant submanifold in a sphere S 2 n + 1 with ε = 1 and ϕ = 2 .

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 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.

On pseudo-slant submanifolds of a Sasakian space form

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5909-5919
Author(s):  
Süleyman Dirik ◽  
Mehmet Atçeken ◽  
Ümit Yıldırım
Keyword(s):  
Space Form ◽  
Sufficient Conditions ◽  
Sasakian Space Form ◽  
Sasakian Manifolds ◽  
Space Forms ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Slant Submanifolds ◽  
Sasakian Space Forms ◽  
Necessary And Sufficient

In this paper, we study the geometry of the pseudo-slant submanifolds of a Sasakian space form. Necessary and sufficient conditions are given for a submanifold to be pseudo-slant submanifolds, pseudo-slant product, mixed geodesic and totally geodesic in Sasakian manifolds. Finally, we give some results for totally umbilical pseudo-slant submanifolds of Sasakian manifolds and Sasakian space forms.

scholarly journals Classification of warped product pointwise semi-slant submanifolds in complex space forms

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5273-5290
Author(s):  
Akram Ali ◽  
Ali Alkhaldi ◽  
Jae Lee ◽  
Wan Othman
Keyword(s):  
Warped Product ◽  
Complex Space ◽  
Space Form ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Slant Submanifold ◽  
Space Forms ◽  
Riemannian Product ◽  
Necessary And Sufficient ◽  
Complex Space Forms

The main principle of this paper is to show that, a warped product pointwise semi-slant submanifold of type Mn = Nn1 T xf Nn2? in a complex space form ?M2m (C) admitting shrinking or steady gradient Ricci soliton, whose potential function is a well-define warped function, is an Einstein warped product pointwise semi-slant submanifold under extrinsic restrictions on the second fundamental form inequality attaining the equality in [4]. Moreover, under some geometric assumption, the connected and compactness with nonempty boundary are treated. In this case, we propose a necessary and sufficient condition in terms of Dirichlet energy function which show that a connected, compact warped product pointwise semi-slant submanifold of complex space forms must be a Riemannian product. As more applications, for the first one, we prove that Mn is a trivial compact warped product, when the warping function exist the solution of PDE such as Euler-Lagrange equation. In the second one, by imposing boundary conditions, we derive a necessary and sufficient condition in terms of Ricci curvature, and prove that, a compact warped product pointwise semi-slant submanifold Mn of a complex space form, is either a CR warped product or just a usual Riemannian product manifold. We also discuss some obstructions to these constructions in more details.

scholarly journals Ricci curvature on warped product submanifolds of Sasakian-space-forms

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 3917-3930
Author(s):  
Pradip Mandal ◽  
Tanumoy Pal ◽  
Shyamal Hui
Keyword(s):  
Ricci Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Space Form ◽  
Warping Function ◽  
Sasakian Space Form ◽  
Curvature Invariant ◽  
Space Forms ◽  
Slant Submanifolds ◽  
Sasakian Space Forms

The paper deals with the study of Ricci curvature on warped product pointwise bi-slant submanifolds of Sasakian-space-form. We obtained some inequalities for such submanifold involving intrinsic invariant, namely the Ricci curvature invariant and extrinsic invariant, namely the squared mean curvature invariant. Some relations of Hamiltonian, Lagrangian and Hessian tensor of warping function are studied here.

scholarly journals Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Dae Ho Jin
Keyword(s):  
Vector Field ◽  
Space Form ◽  
Sasakian Manifold ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Structure ◽  
Sasakian Space Forms ◽  
Generalized Sasakian Space Form ◽  
Characterization Theorems ◽  
Lightlike Hypersurfaces

We study lightlike hypersurfacesMof an indefinite generalized Sasakian space formM-(f1,f2,f3), with indefinite trans-Sasakian structure of type(α,β), subject to the condition that the structure vector field ofM-is tangent toM. First we study the general theory for lightlike hypersurfaces of indefinite trans-Sasakian manifold of type(α,β). Next we prove several characterization theorems for lightlike hypersurfaces of an indefinite generalized Sasakian space form.

Symmetry properties of complex contact space form

2019 ◽  
pp. 2050157 ◽  
Author(s):  
Mohamed Belkhelfa ◽  
Fatima Zohra Kadi
Keyword(s):  
Space Form ◽  
Einstein Manifold ◽  
Contact Manifold ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Symmetry Properties ◽  
Symmetric Complex ◽  
Complex Contact Manifold ◽  
Contact Space

It is well known that a Sasakian space form is pseudo-symmetric [M. Belkhelfa, R. Deszcz and L. Verstraelen, Symmetry properties of Sasakian space-forms, Soochow J. Math. 31(4) (2005) 611–616], therefore it is Ricci-pseudo-symmetric. In this paper, we proved that a normal complex contact manifold is Ricci-semi-symmetric if and only if it is an Einstein manifold; moreover, we showed that a complex contact space form [Formula: see text] with constant [Formula: see text]-sectional curvature [Formula: see text] is properly Ricci-pseudo-symmetric [Formula: see text] if and only if [Formula: see text]; in this case [Formula: see text]. We gave an example of properly Ricci-pseudo-symmetric complex contact space form. On the other hand, we proved the non-existence of proper pseudo-symmetric ([Formula: see text]) complex contact space form [Formula: see text]

scholarly journals Quasi-Einstein Hypersurfaces of Complex Space Forms

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiaomin Chen ◽  
Xuehui Cui
Keyword(s):  
Real Hypersurface ◽  
Complex Space ◽  
Space Form ◽  
Ricci Soliton ◽  
Complex Space Form ◽  
Einstein Metric ◽  
Space Forms ◽  
The Real ◽  
Complex Euclidean Space ◽  
Complex Space Forms

Based on a well-known fact that there are no Einstein hypersurfaces in a nonflat complex space form, in this article, we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hypersurface of a nonflat complex space form. For the real hypersurface with quasi-Einstein metric of a complex Euclidean space, we also give a classification. Since a gradient Ricci soliton is a special quasi-Einstein metric, our results improve some conclusions of Cho and Kimura.

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