scholarly journals LIGHTLIKE HYPERSURFACES OF AN INDEFINITE GENERALIZED SASAKIAN SPACE FORM WITH A SYMMETRIC METRIC CONNECTION OF TYPE (ℓ, m)

2016 ◽  
Vol 31 (3) ◽  
pp. 613-624
Author(s):  
Dae Ho Jin
Keyword(s):  
Space Form ◽  
Sasakian Space Form ◽  
Metric Connection ◽  
Generalized Sasakian Space Form ◽  
Lightlike Hypersurfaces

scholarly journals Characterizations of the Total Space (Indefinite Trans-Sasakian Manifolds) Admitting a Semi-Symmetric Metric Connection

Axioms ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 68
Author(s):  
Dae Jin ◽  
Jae Lee
Keyword(s):  
Space Form ◽  
Sasakian Manifold ◽  
Total Space ◽  
Sasakian Space Form ◽  
Sasakian Manifolds ◽  
Metric Connection ◽  
Generalized Sasakian Space Form ◽  
Lightlike Hypersurfaces ◽  
Kenmotsu Space Form

We investigate recurrent, Lie-recurrent, and Hopf lightlike hypersurfaces of an indefinite trans-Sasakian manifold with a semi-symmetric metric connection. In these hypersurfaces, we obtain several new results. Moreover, we characterize that the total space (an indefinite generalized Sasakian space form) with a semi-symmetric metric connection is an indefinite Kenmotsu space form under various lightlike hypersurfaces.

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 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 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 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.

Symmetries of Sasakian Generalized Sasakian-Space-Form Admitting Generalized Tanaka–Webster Connection

2021 ◽  
Vol 52 ◽  
Author(s):  
Chawngthu Lalmalsawma ◽  
Jay Prakash Singh
Keyword(s):  
Space Form ◽  
Sasakian Space Form ◽  
Generalized Sasakian Space Form ◽  
Symmetric Properties

The object of this paper is to study symmetric properties of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. We studied semisymmetry and Ricci semisymmetry of Sasakian generalized Sasakian-space-form with respect to generalized Tanaka–Webster connection. Further we obtain results for Ricci pseudosymmetric and Ricci-generalized pseudosymmetric Sasakian generalized Sasakian-space-form.

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