scholarly journals On an (ε,δ)-trans-Sasakian structure

2012 ◽  
Vol 61 (1) ◽  
pp. 20 ◽  
Author(s):  
H G Nagaraja ◽  
R C Premalatha ◽  
G Somashekara
Keyword(s):  
Sasakian Structure

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 Invariance of basic Hodge numbers under deformations of Sasakian manifolds

2020 ◽  
Author(s):  
Paweł Raźny
Keyword(s):  
Elliptic Operators ◽  
Holomorphic Foliation ◽  
Sasakian Manifolds ◽  
Contact Manifolds ◽  
Continuity Theorem ◽  
Riemannian Foliations ◽  
Holomorphic Structure ◽  
Sasakian Structure ◽  
Hodge Numbers ◽  
Small Deformations

Abstract We show that the Hodge numbers of Sasakian manifolds are invariant under arbitrary deformations of the Sasakian structure. We also present an upper semi-continuity theorem for the dimensions of kernels of a smooth family of transversely elliptic operators on manifolds with homologically orientable transversely Riemannian foliations. We use this to prove that the $$\partial {\bar{\partial }}$$ ∂ ∂ ¯ -lemma and being transversely Kähler are rigid properties under small deformations of the transversely holomorphic structure which preserve the foliation. We study an example which shows that this is not the case for arbitrary deformations of the transversely holomorphic foliation. Finally we point out an application of the upper-semi continuity theorem to K-contact manifolds.

scholarly journals On totally umbilical QR-submanifolds of quaternion Kaehlerian manifolds

2000 ◽  
Vol 62 (1) ◽  
pp. 95-103 ◽  
Author(s):  
Aurel Bejancu ◽  
Hani Reda Farran
Keyword(s):  
Totally Geodesic ◽  
Totally Umbilical ◽  
Sasakian Structure ◽  
Kaehlerian Manifold ◽  
Extrinsic Sphere

We introduce the notion of generalised 3-Sasakian structure on a manifold and show that a totally umbilical, but not totally geodesic, proper QR-submanifold of a quaternion Kaehlerian manifold is an extrinsic sphere and inherits such a structure.

scholarly journals On Lightlike Geometry of Para-Sasakian Manifolds

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Bilal Eftal Acet ◽  
Selcen Yüksel Perktaş ◽  
Erol Kılıç
Keyword(s):  
Vector Field ◽  
Characteristic Vector ◽  
Sasakian Manifolds ◽  
Lightlike Hypersurface ◽  
Sasakian Structure ◽  
Integrability Conditions ◽  
Integrable Distribution ◽  
Lightlike Hypersurfaces ◽  
Characteristic Vector Field

We study lightlike hypersurfaces of para-Sasakian manifolds tangent to the characteristic vector field. In particular, we define invariant lightlike hypersurfaces and screen semi-invariant lightlike hypersurfaces, respectively, and give examples. Integrability conditions for the distributions on a screen semi-invariant lightlike hypersurface of para-Sasakian manifolds are investigated. We obtain a para-Sasakian structure on the leaves of an integrable distribution of a screen semi-invariant lightlike hypersurface.

scholarly journals Indefinite Almost Paracontact Metric Manifolds

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Mukut Mani Tripathi ◽  
Erol Kılıç ◽  
Selcen Yüksel Perktaş ◽  
Sadık Keleş
Keyword(s):  
Riemannian Manifold ◽  
Sectional Curvature ◽  
Curvature Tensor ◽  
Ricci Tensor ◽  
Sasakian Manifold ◽  
Constant Sectional Curvature ◽  
Sasakian Manifolds ◽  
Sasakian Structure

We introduce the concept of (ε)-almost paracontact manifolds, and in particular, of (ε)-para-Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it cannot admit an (ε)-para Sasakian structure. We show that, for an (ε)-para Sasakian manifold, the conditions of being symmetric, semi-symmetric, or of constant sectional curvature are all identical. It is shown that a symmetric spacelike (resp., timelike) (ε)-para Sasakian manifoldMnis locally isometric to a pseudohyperbolic spaceHνn(1)(resp., pseudosphereSνn(1)). At last, it is proved that for an (ε)-para Sasakian manifold the conditions of being Ricci-semi-symmetric, Ricci-symmetric, and Einstein are all identical.

Classification of slant surfaces in 𝕊3 × ℝ

2020 ◽  
Vol 20 (4) ◽  
pp. 463-472
Author(s):  
Salvatore de Candia ◽  
Marian Ioan Munteanu
Keyword(s):  
Vector Field ◽  
Hermitian Manifold ◽  
Complex Surfaces ◽  
Almost Hermitian Manifold ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Sasakian Structure ◽  
First Case ◽  
Totally Real

AbstractWe investigate slant surfaces in the almost Hermitian manifold 𝕊3 × ℝ, considering the position of the Reeb vector field ξ of the Sasakian structure on 𝕊3 with respect to the surfaces. We examine two cases: ξ normal or tangent to the surfaces. In the first case, we prove that every surface is totally real. In the second case, we characterize and locally describe complex surfaces. Finally, we completely classify non-complex slant surfaces, giving explicit examples.

scholarly journals ON 3-DIMENSIONAL ($\epsilon$,$\delta$)-TRANS-SASAKIAN STRUCTURE

2013 ◽  
Vol 87 (3) ◽  
Author(s):  
Y.B. Maralabhavi ◽  
G.S. Shivaprasanna ◽  
G. Somashekhara
Keyword(s):  
3 Dimensional ◽  
Sasakian Structure
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