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 TOTALLY UMBILICAL SEMI-INVARIANT SUBMANIFOLDS AND CR-SUBMANIFOLDS OF A SASAKIAN MANIFOLD

1993 ◽  
Vol 24 (2) ◽  
pp. 161-172
Author(s):  
S. M. KHURSEED HAIDER ◽  
V. A. KHAN ◽  
S. I. HUSAIN
Keyword(s):  
Space Form ◽  
Sasakian Manifold ◽  
Classification Theorem ◽  
Sasakian Space Form ◽  
Invariant Submanifold ◽  
Totally Umbilical ◽  
Cr Submanifold ◽  
Invariant Submanifolds ◽  
Cr Submanifolds

In the present paper, a classification theorem for totally um- bilical semi-invariant submanifold is established. CR-submanifolds of a Sasakian space form are studied in detail, and finally a theorem for a CR- submanifold of a Sasakian manifold to be a proper contact CR-product is proved.

scholarly journals Semi-invariant submanifolds of Lorentzian Sasakian manifolds

2011 ◽  
Vol 44 (2) ◽  
Author(s):  
Pablo Alegre
Keyword(s):  
Space Form ◽  
Contact Manifold ◽  
Sasakian Manifold ◽  
Sasakian Space Form ◽  
Sasakian Manifolds ◽  
Principal Characteristics ◽  
Almost Contact Manifold ◽  
Invariant Submanifolds

AbstractIn this paper we introduce the notion of semi-invariant submanifolds of a Lorentzian almost contact manifold. We study their principal characteristics and the particular cases in which the manifold is a Lorentzian Sasakian manifold or a Lorentzian 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.

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