Automorphisms and a reduction theorem in a Sasakian space form E2m+1(−3)

1986 ◽  
Vol 145 (1) ◽  
pp. 317-336
Author(s):  
Shōichi Funabashi
Keyword(s):  
Space Form ◽  
Reduction Theorem ◽  
Sasakian Space Form

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]

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 RICCI SOLITONS ON HOPH HYPERSURFACES IN SASAKIAN SPACE FORM

2017 ◽  
pp. 387
Author(s):  
Zahra Nazari ◽  
Esmail Abedi
Keyword(s):  
Space Form ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Principal Curvatures ◽  
Sasakian Space Form ◽  
Potential Vector

We are studying Ricci solitons on Hoph hypersurfaces in Sasakian space formfM2n+1(c). The rst, we prove that Hoph hypersurfaces of a Sasakian space formfM2n+1(c < 1) with two distinct principal curvatures is shrinking and for c 1,Hoph hypersurfaces with two distinct principal curvatures of a Sasakian space formfM2n+1(c) does not admit a Ricci soliton. We show that there is not any Hoph hyper-surfaces with two distinct principal curvatures in a Sasakian space form fM2n+1(c)with a -Ricci soliton (and Ricci soliton) such that potential vector eld is the Reebvector eld.Then we prove that Hoph hypersurfaces in Sasakian space form fM2n+1(c) withc = 1 does not admit a - Ricci soliton with potential vector eld U and we showthat Ricci soliton on Hoph hypersurfaces M in Sasakian space form fM2n+1(c <

scholarly journals Semi-invariant submanifolds of a Sasakian space form

1984 ◽  
Vol 48 (2) ◽  
pp. 229-240 ◽  
Author(s):  
Aurel Bejancu ◽  
Neculai Papaghiuc
Keyword(s):  
Space Form ◽  
Sasakian Space Form ◽  
Invariant Submanifolds

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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