scholarly journals Contact totally umbilical submanifolds of a sasakian space form

1977 ◽  
Vol 114 (1) ◽  
pp. 351-364 ◽  
Author(s):  
Ikuo Ishihara ◽  
Masahiro Kon
Keyword(s):  
Space Form ◽  
Sasakian Space Form ◽  
Totally Umbilical ◽  
Totally Umbilical 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.

On pseudo-slant submanifolds of a Sasakian space form

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5909-5919
Author(s):  
Süleyman Dirik ◽  
Mehmet Atçeken ◽  
Ümit Yıldırım
Keyword(s):  
Space Form ◽  
Sufficient Conditions ◽  
Sasakian Space Form ◽  
Sasakian Manifolds ◽  
Space Forms ◽  
Totally Geodesic ◽  
Totally Umbilical ◽  
Slant Submanifolds ◽  
Sasakian Space Forms ◽  
Necessary And Sufficient

In this paper, we study the geometry of the pseudo-slant submanifolds of a Sasakian space form. Necessary and sufficient conditions are given for a submanifold to be pseudo-slant submanifolds, pseudo-slant product, mixed geodesic and totally geodesic in Sasakian manifolds. Finally, we give some results for totally umbilical pseudo-slant submanifolds of Sasakian manifolds and Sasakian space forms.

scholarly journals TOTALLY UMBILICAL SUBMANIFOLDS OF A COMPLEX SPACE FORM

1991 ◽  
Vol 22 (1) ◽  
pp. 105-106
Author(s):  
SHAHID ALI ◽  
VIQAR AZAM KHAN
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Totally Umbilical ◽  
Totally Umbilical Submanifolds

TOTALLY UMBILICAL SUBMANIFOLDS OF A COMPLEX 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]

Conformal Killing Forms on Totally Umbilical Submanifolds

2016 ◽  
Vol 217 (5) ◽  
pp. 525-539 ◽  
Author(s):  
S. E. Stepanov ◽  
I. A. Alexandrova ◽  
I. I. Tsyganok ◽  
J. Mikeš
Keyword(s):  
Conformal Killing ◽  
Totally Umbilical ◽  
Totally Umbilical Submanifolds
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