scholarly journals A Basic Inequality for the Tanaka-Webster Connection

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Dae Ho Jin ◽  
Jae Won Lee
Keyword(s):  
Vector Field ◽  
Ricci Curvature ◽  
Mean Curvature ◽  
Space Form ◽  
The Other ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Basic Inequality

For submanifolds tangent to the structure vector field in Sasakian space forms, we establish a Chen's basic inequality between the main intrinsic invariants of the submanifold (namely, its pseudosectional curvature and pseudosectional curvature on one side) and the main extrinsic invariant (namely, squared pseudomean curvature on the other side) with respect to the Tanaka-Webster connection. Moreover, involving the pseudo-Ricci curvature and the squared pseudo-mean curvature, we obtain a basic inequality for submanifolds of a Sasakian space form tangent to the structure vector field in terms of the Tanaka-Webster connection.

scholarly journals A basic inequality for submanifolds in a cosymplectic space form

2003 ◽  
Vol 2003 (9) ◽  
pp. 539-547 ◽  
Author(s):  
Jeong-Sik Kim ◽  
Jaedong Choi
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Sectional Curvature ◽  
Mean Curvature ◽  
Space Form ◽  
The Other ◽  
Space Forms ◽  
Basic Inequality

For submanifolds tangent to the structure vector field in cosymplectic space forms, we establish a basic inequality between the main intrinsic invariants of the submanifold, namely, its sectional curvature and scalar curvature on one side; and its main extrinsic invariant, namely, squared mean curvature on the other side. Some applications, including inequalities between the intrinsic invariantδMand the squared mean curvature, are given. The equality cases are also discussed.

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.

scholarly journals A class of C-totally real submanifolds of Sasakian space forms

1998 ◽  
Vol 65 (1) ◽  
pp. 120-128
Author(s):  
Filip Defever ◽  
Ion Mihai ◽  
Leopold Verstraelen
Keyword(s):  
Riemannian Manifold ◽  
Mean Curvature ◽  
Space Form ◽  
Sasakian Space Form ◽  
Real Submanifolds ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Totally Real ◽  
Real Complex

AbstractRecently, Chen defined an invariant δM of a Riemannian manifold M. Sharp inequalities for this Riemannian invariant were obtained for submanifolds in real, complex and Sasakian space forms, in terms of their mean curvature. In the present paper, we investigate certain C-totally real submanifolds of a Sasakian space form M2m+1(C)satisfying Chen's equality.

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 B.-Y. Chen inequalities for semislant submanifolds in Sasakian space forms

2003 ◽  
Vol 2003 (27) ◽  
pp. 1731-1738 ◽  
Author(s):  
Dragoş Cioroboiu
Keyword(s):  
Vector Field ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Sasakian Manifold ◽  
Sharp Inequality ◽  
Space Forms ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Sasakian Space Forms ◽  
Riemannian Space Forms

Chen (1993) established a sharp inequality for the sectional curvature of a submanifold in Riemannian space forms in terms of the scalar curvature and squared mean curvature. The notion of a semislant submanifold of a Sasakian manifold was introduced by J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, and M. Fernandez (1999). In the present paper, we establish Chen inequalities for semislant submanifolds in Sasakian space forms by using subspaces orthogonal to the Reeb vector fieldξ.

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 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.

Geodesic spheres and Jacobi vector fields on Sasakian space forms

1987 ◽  
Vol 105 (1) ◽  
pp. 17-22 ◽  
Author(s):  
David E. Blair ◽  
Lieven Vanhecke
Keyword(s):  
Vector Fields ◽  
Space Form ◽  
Shape Operator ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Geodesic Spheres ◽  
Jacobi Vector

SynopsisUsing explicit equations for Jacobi vector fields on a Sasakian space form, we characterise such spaces by means of the shape operator of small geodesic spheres.

scholarly journals Some Curvature Properties on Lorentzian Generalized Sasakian-Space-Forms

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Rongsheng Ma ◽  
Donghe Pei
Keyword(s):  
Space Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Conformally Flat ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Projectively Flat ◽  
Generalized Sasakian Space Form ◽  
Necessary And Sufficient

In this paper, we investigate the Lorentzian generalized Sasakian-space-form. We give the necessary and sufficient conditions for the Lorentzian generalized Sasakian-space-form to be projectively flat, conformally flat, conharmonically flat, and Ricci semisymmetric and their relationship between each other. As the application of our theorems, we study the Ricci almost soliton on conformally flat Lorentzian generalized Sasakian-space-form.

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