Normal CR structures on compact 3-manifolds

By F. Belgun. 2000

48 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/41c4b424f2a73198ff1a275ef64b03dded7d0f3c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Misha Verbitsky
2. L. Ornea
3. Anna Fino
4. Luigi Vezzoni

In Geometry and Topology

1. Misha Verbitsky
2. L. Ornea
3. D. Huybrechts
4. Nicolas Addington
5. Benjamin Bakker
6. C. Lehn
7. Anna Fino
8. Luigi Vezzoni

Citations in the corpus

• On the existence of almost contact structure and the contact magnetic field (2009, unknown): “In fact, any compact Sasakian manifold is a Seifert fibration but the Sasakian structures can be explicitly described [3].”
• Sasakian structures on CR-manifolds (2006, background): “6 In dimension 3, Sasakian structures on CR-manifolds were completely classified [3,4,11].”