On three-dimensional generalized sasakian space –forms

2012 ◽  
Vol 5 (1) ◽  
Author(s):  
S. Yadav
Keyword(s):  
Three Dimensional ◽  
Space Forms ◽  
Sasakian Space Forms

scholarly journals f-Biharmonic Curves in the Three-dimensional Para-Sasakian Space Forms

2021 ◽  
pp. 369-379
Author(s):  
Murat Altunbaş
Keyword(s):  
Three Dimensional ◽  
Space Forms ◽  
3 Dimensional ◽  
Sasakian Space Forms ◽  
Sasakian Structures ◽  
Biharmonic Curves

In this paper, we give some characterizations for proper f-biharmonic curves in the para-Bianchi-Cartan-Vranceanu space forms with 3-dimensional para-Sasakian structures.

On three dimensional generalized Sasakian-space-forms

2017 ◽  
Vol 108 (3) ◽  
pp. 1039-1053
Author(s):  
Pradip Majhi ◽  
Uday Chand De
Keyword(s):  
Three Dimensional ◽  
Space Forms ◽  
Sasakian Space Forms

Unitary vector fields are Fermi–Walker transported along Rytov–Legendre curves

2015 ◽  
Vol 12 (10) ◽  
pp. 1550111 ◽  
Author(s):  
Mircea Crasmareanu ◽  
Camelia Frigioiu
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Ricci Soliton ◽  
Conformal Killing ◽  
Space Forms ◽  
Potential Vector ◽  
Legendre Curves ◽  
Complex Space Forms

Fix ξ a unitary vector field on a Riemannian manifold M and γ a non-geodesic Frenet curve on M satisfying the Rytov law of polarization optics. We prove in these conditions that γ is a Legendre curve for ξ if and only if the γ-Fermi–Walker covariant derivative of ξ vanishes. The cases when γ is circle or helix as well as ξ is (conformal) Killing vector filed or potential vector field of a Ricci soliton are analyzed and an example involving a three-dimensional warped metric is provided. We discuss also K-(para)contact, particularly (para)Sasakian, manifolds and hypersurfaces in complex space forms.

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.

Stability of Biharmonic Legendrian Submanifolds in Sasakian Space Forms

2008 ◽  
Vol 51 (3) ◽  
pp. 448-459 ◽  
Author(s):  
Toru Sasahara
Keyword(s):  
Critical Points ◽  
Harmonic Map ◽  
Biharmonic Maps ◽  
Space Forms ◽  
Sasakian Space Forms ◽  
The Stability ◽  
Biharmonic Map ◽  
Legendrian Submanifolds

AbstractBiharmonic maps are defined as critical points of the bienergy. Every harmonic map is a stable biharmonic map. In this article, the stability of nonharmonic biharmonic Legendrian submanifolds in Sasakian space forms is discussed.

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