On the induced almost contact structure of a Brieskorn manifold

1977 ◽  
Vol 6 (4) ◽  
Author(s):  
Toyoko Kashiwada
Keyword(s):  
Contact Structure ◽  
Almost Contact Structure ◽  
Brieskorn Manifold

scholarly journals On the existence of almost contact structure and the contact magnetic field

2009 ◽  
Vol 125 (1-2) ◽  
pp. 191-199 ◽  
Author(s):  
J. L. Cabrerizo ◽  
M. Fernández ◽  
J. S. Gómez
Keyword(s):  
Magnetic Field ◽  
Contact Structure ◽  
Almost Contact Structure

scholarly journals On differentiable manifolds with certain structures which are closely related to almost contact structure, II

1961 ◽  
Vol 13 (2) ◽  
pp. 281-294 ◽  
Author(s):  
Shigeo Sasaki ◽  
Yoji Hatakeyama
Keyword(s):  
Contact Structure ◽  
Differentiable Manifolds ◽  
Almost Contact Structure

ON FINSLER MANIFOLDS WHOSE TANGENT BUNDLE HAS THE g-NATURAL METRIC

2011 ◽  
Vol 08 (07) ◽  
pp. 1593-1610 ◽  
Author(s):  
ESMAEIL PEYGHAN ◽  
AKBAR TAYEBI
Keyword(s):  
Riemannian Manifold ◽  
Constant Curvature ◽  
Positive Constant ◽  
Tangent Bundle ◽  
Contact Structure ◽  
Jacobi Operator ◽  
Riemannian Metric ◽  
Finsler Manifolds ◽  
Almost Contact Structure ◽  
Flat Riemannian Manifold

In this paper, we introduce a Riemannian metric [Formula: see text] and a family of framed f-structures on the slit tangent bundle [Formula: see text] of a Finsler manifold Fn = (M, F). Then we prove that there exists an almost contact structure on the tangent bundle, when this structure is restricted to the Finslerian indicatrix. We show that this structure is Sasakian if and only if Fn is of positive constant curvature 1. Finally, we prove that (i) Fn is a locally flat Riemannian manifold if and only if [Formula: see text], (ii) the Jacobi operator [Formula: see text] is zero or commuting if and only if (M, F) have the zero flag curvature.

Normal Variations of Invariant Hypersurfaces of Framed Manifolds

1972 ◽  
Vol 15 (4) ◽  
pp. 513-521
Author(s):  
Samuel I. Goldberg
Keyword(s):  
Complex Manifold ◽  
Contact Structure ◽  
Complex Structure ◽  
Almost Complex Structure ◽  
Marked Contrast ◽  
Almost Complex Manifold ◽  
Almost Contact Structure ◽  
Almost Complex ◽  
Differentiable Vector ◽  
Real Codimension

A hypersurface of a globally framed f-manifold (briefly, a framed manifold), does not in general possess a framed structure as one may see by considering the 4-sphere S4 in R5 or S5. For, a hypersurface so endowed carries an almost complex structure, or else, it admits a nonsingular differentiable vector field. Since an almost complex manifold may be considered as being globally framed, with no complementary frames, this situation is in marked contrast with the well known fact that a hypersurface (real codimension 1) of an almost complex manifold admits a framed structure, more specifically, an almost contact structure.

scholarly journals Real hypersurfaces with an induced almost contact structure

2009 ◽  
Vol 114 (1) ◽  
pp. 41-51 ◽  
Author(s):  
Michał Szancer ◽  
Zuzanna Szancer
Keyword(s):  
Contact Structure ◽  
Real Hypersurfaces ◽  
Almost Contact Structure

scholarly journals On Subcritically Stein Fillable 5-manifolds

2018 ◽  
Vol 61 (1) ◽  
pp. 85-96 ◽  
Author(s):  
Fan Ding ◽  
Hansjörg Geiges ◽  
Guangjian Zhang
Keyword(s):  
Fundamental Group ◽  
Contact Structure ◽  
Contact Structures ◽  
Homotopy Classification ◽  
Contact Manifolds ◽  
Almost Contact Structure ◽  
Diffeomorphism Type ◽  
Standard Contact ◽  
Simply Connected

AbstractWe make some elementary observations concerning subcritically Stein fillable contact structures on 5-manifolds. Specifically, we determine the diffeomorphism type of such contact manifolds in the case where the fundamental group is finite cyclic, and we show that on the 5-sphere, the standard contact structure is the unique subcritically ?llable one. More generally, it is shown that subcritically fillable contact structures on simply connected 5-manifolds are determined by their underlying almost contact structure. Along the way, we discuss the homotopy classification of almost contact structures.

On a type of K-contact Riemannian manifold

1972 ◽  
Vol 13 (4) ◽  
pp. 447-450 ◽  
Author(s):  
M. C. Chaki ◽  
D. Ghosh
Keyword(s):  
Vector Field ◽  
Contact Structure ◽  
Contact Manifold ◽  
Riemannian Metric ◽  
Positive Definite ◽  
Almost Contact Metric Structure ◽  
Almost Contact Structure ◽  
Almost Contact Metric ◽  
Contact Metric Structure ◽  
Image Position

Let M be an n-dimensional (n = 2m + 1, m ≦ 1) real differentiable manifold. if on M there exist a tensor field , a contravariant vector field ξi and a convariant vector field ηi such that then M is said to have an almost contact structure with the structure tensors (φ,ξ, η) [1], [2]. Further, if a positive definite Riemannian metric g satisfies the conditions then g is called an associated Riemannian metric to the almost contact structure and M is then said to have an almost contact metric structure. On the other hand, M is said to have a contact structure [2], [4] if there exists a 1-form η over M such that η ∧ (dη)m ≠ 0 everywhere over M where dη means the exterior derivation of η and the symbol ∧ means the exterior multiplication. In this case M is said to be a contact manifold with contact form η. It is known [2, Th. 3,1] that if η = ηidxi is a 1-form defining a contact structure, then there exists a positive definite Riemannian metric in gij such that and define an almost contact metric structure with and ηi where the symbol ∂i standing for ∂/∂xi.

scholarly journals On the existence of a complex almost contact structure

1978 ◽  
Vol 1 (2) ◽  
pp. 197-204 ◽  
Author(s):  
Yhuji Shibuya
Keyword(s):  
Contact Structure ◽  
Almost Contact Structure

scholarly journals On the integrability of almost contact structure

1962 ◽  
Vol 14 (2) ◽  
pp. 167-176 ◽  
Author(s):  
Shigeo Sasaki ◽  
Chen-jung Hsu
Keyword(s):  
Contact Structure ◽  
Almost Contact Structure
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