scholarly journals Da-Homothetic Deformation of K-Contact Manifolds

ISRN Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
H. G. Nagaraja ◽  
C. R. Premalatha
Keyword(s):  
Scalar Curvature ◽  
Space Form ◽  
Contact Manifold ◽  
Sasakian Space Form ◽  
Contact Manifolds ◽  
Generalized Sasakian Space Form

We study Da-homothetic deformations of K-contact manifolds. We prove that Da-homothetically deformed K-contact manifold is a generalized Sasakian space form if it is conharmonically flat. Further, we find expressions for scalar curvature of Da-homothetically deformed K-contact manifolds.

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 Strongly pseudo-convex CR space forms

2019 ◽  
Vol 6 (1) ◽  
pp. 279-293 ◽  
Author(s):  
Jong Taek Cho
Keyword(s):  
Sectional Curvature ◽  
Hyperbolic Space ◽  
Space Form ◽  
Contact Manifold ◽  
Holomorphic Sectional Curvature ◽  
Sphere Bundle ◽  
Sasakian Space Form ◽  
Space Forms ◽  
Pseudo Convex ◽  
Unit Tangent Sphere Bundle

AbstractFor a contact manifold, we study a strongly pseudo-convex CR space form with constant holomorphic sectional curvature for the Tanaka-Webster connection. We prove that a strongly pseudo-convex CR space form M is weakly locally pseudo-Hermitian symmetric if and only if (i) dim M = 3, (ii) M is a Sasakian space form, or (iii) M is locally isometric to the unit tangent sphere bundle T1(𝔿n+1) of a hyperbolic space 𝔿n+1 of constant curvature −1.

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 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.

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 Ricci soliton and η-Ricci soliton on Generalized Sasakian space form

Filomat ◽  
2017 ◽  
Vol 31 (13) ◽  
pp. 4051-4062 ◽  
Author(s):  
Sampa Pahan ◽  
Tamalika Dutta ◽  
Arindam Bhattacharyya
Keyword(s):  
Space Form ◽  
Ricci Soliton ◽  
Sasakian Space Form ◽  
Generalized Sasakian Space Form
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