Niveau: Supérieur, Doctorat, Bac+8
QUASI-CONTACT S-R METRICS: NORMAL FORM IN R2n, WAVE FRONT AND CAUSTIC IN R4 G. CHARLOT? ? Laboratoire GTA, Universite de Montpellier II, 34095, Montpellier cedex 5, France. E-mail: Abstract This paper deals with sub-Riemannian metrics in the quasi-contact case. First, in any even dimension, we construct normal coordinates, a normal form and invariants, which are the analogs of normal coordinates, normal form and classical invariants in Riemannian geometry. Second, in dimension 4, and thanks to this ”normal form”, we study the local singularities of the exponential map. 1. Introduction This paper is a continuation of a series of papers ([C-G-K], [A-C-G-K], [A-C-G], [A-G], [A-C-G-Z]) dealing with contact metrics. In these papers, the authors con- struct normal coordinates, a canonical field of normal frames and invariant tensors. These objects are the analogs of normal coordinates, normal frame and classical invariant tensors (such as the curvature tensor) in Riemannian geometry. They do this in any odd dimension. They also study in details the exponential map, the wave-front, the cut locus and the conjugate locus in dimension 3.
- struct normal
- normal coordinates
- riemannian
- distribution defined
- upper conjugate
- dimensional contact
- unique natural normal