scholarly journals Inequalities on Generalized Sasakian Space Forms

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Najma Abdul Rehman ◽  
Abdul Ghaffar ◽  
Esmaeil Abedi ◽  
Mustafa Inc ◽  
Mohammed K. A. Kaabar
Keyword(s):  
Space Form ◽  
Variational Formula ◽  
Stability Criteria ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Metric Connection ◽  
Generalized Sasakian Space Form ◽  
The Stability ◽  
Second Variational Formula

In this paper, we find the second variational formula for a generalized Sasakian space form admitting a semisymmetric metric connection. Inequalities regarding the stability criteria of a compact generalized Sasakian space form admitting a semisymmetric metric connection are established.

GENERALIZED SASAKIAN SPACE FORMS WITH SEMI-SYMMETRIC METRIC CONNECTIONS

2014 ◽  
Vol 60 (1) ◽  
pp. 145-156
Author(s):  
Sibel Sular ◽  
Cihan Özgur
Keyword(s):  
Existence Theorem ◽  
Space Form ◽  
Warped Products ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
Metric Connection ◽  
Generalized Sasakian Space Form

Abstract The aim of the present paper is to introduce generalized Sasakian space forms endowed with semi-symmetric metric connections. We obtain the existence theorem of a generalized Sasakian space form with semi-symmetric metric connection and we give some examples by using warped products endowed with semi-symmetric metric connection.

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 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.

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.

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]

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 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 On interpolating sesqui-harmonic Legendre curves in Sasakian space forms

2019 ◽  
Vol 17 (01) ◽  
pp. 2050005 ◽  
Author(s):  
Fatma Karaca ◽  
Cihan Özgür ◽  
Uday Chand De
Keyword(s):  
Space Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Legendre Curve ◽  
Sasakian Space Forms ◽  
Legendre Curves ◽  
Necessary And Sufficient

We consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms. We find the necessary and sufficient conditions for Legendre curves in Sasakian space forms to be interpolating sesqui-harmonic. Finally, we obtain a proper example for an interpolating sesqui-harmonic Legendre curve in a Sasakian space form.

scholarly journals Characterizing inequalities for existence of contact CR-warped product submanifolds of generalized Sasakian space forms admitting a nearly cosymplectic structure

2022 ◽  
Vol 40 ◽  
pp. 1-11
Author(s):  
Meraj Ali Khan
Keyword(s):  
Warped Product ◽  
Second Fundamental Form ◽  
Warping Function ◽  
Sasakian Space Form ◽  
Space Forms ◽  
The Second Fundamental Form ◽  
Cosymplectic Structure ◽  
Sasakian Space Forms ◽  
Generalized Sasakian Space Form ◽  
Nearly Cosymplectic

This paper studies the contact CR-warped product submanifolds of a generalized Sasakian space form admitting a nearly cosymplectic structure. Some inequalities for the existence of these types of warped product submanifolds are established, the obtained inequalities generalize the results that have acquired in \cite{atceken14}. Moreover, we also estimate another inequality for the second fundamental form in the expressions of the warping function, this inequality also generalizes the inequalities that have obtained in \cite{ghefari19}. In addition, we also explore the equality cases.

scholarly journals Ricci curvature of contact CR-warped product submanifolds in generalized Sasakian space forms admitting a trans-Sasakian structure

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 125-146
Author(s):  
Meraj Khan ◽  
Cenep Ozel
Keyword(s):  
Ricci Curvature ◽  
Warped Product ◽  
Curvature Vector ◽  
Warping Function ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Sasakian Structure ◽  
Sasakian Space Forms ◽  
Generalized Sasakian Space Form ◽  
Isometric To A Sphere

The objective of this paper is to achieve the inequality for Ricci curvature of a contact CR-warped product submanifold isometrically immersed in a generalized Sasakian space form admitting a trans-Sasakian structure in the expressions of the squared norm of mean curvature vector and warping function. We provide numerous physical applications of the derived inequalities. Finally, we prove that under a certain condition the base manifold is isometric to a sphere with a constant sectional curvature.

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