Showing papers on "Reeb vector field published in 2001"
TL;DR: In this article, the authors studied normal CR compact manifolds in dimension 3 and showed that the underlying manifolds are topologically finite quotients of a non-flat circle bundle over a Riemann surface.
Abstract: We study normal CR compact manifolds in dimension 3. For a choice of a CR Reeb vector field, we associate a Sasakian metric on them, and we classify those metrics. As a consequence, the underlying manifolds are topologically finite quotients of \(S^3\) or of a non-flat circle bundle over a Riemann surface of positive genus. In the latter case, we prove that their CR automorphisms group is a finite extension of \(S^1\), and we classify the normal CR structures on these manifolds.
45 citations
DOI•
01 Jan 2001
TL;DR: In this paper, the authors consider a 3-manifold M equipped with the contact form λ and consider smooth maps u : C → R × M solving the Cauchy-Riemann equations Tu i = J(u) Tu for a distinguished class of almost complex structures J on R ×M which are R-invariant and related to λ.
Abstract: Given a compact 3-manifold M equipped with the contact form λ we consider smooth maps u : C → R × M solving the Cauchy-Riemann equations Tu i = J(u) Tu, for a distinguished class of almost complex structures J on R ×M which are R-invariant and related to λ. If the map is non constant and of finite energy, the projection into M necessarily approaches as |z| → ∞ a periodic solution of the Reeb vector field associated with the contact form. Assuming the periodic solution to be non degenerate we shall describe the asymptotic behavior of the map u. The paper is a revised version of [5] and includes also [6].
11 citations