# Non subanalyticity of sub-Riemannian Martinet spheres

Abstract : Consider the sub-Riemannian Martinet structure $(M,\Delta,g)$ where $M=\R^3$, $\Delta={\rm{Ker }}(dz-{{y^2}\over{2}}dx)$ and $g$ is the general gradated metric of order $0$~: $g=(1+\alpha y)^2dx^2+(1+\beta x+\gamma y)^2dy^2$. We prove that if $\alpha\neq 0$ then the sub-Riemannian spheres $S(0,r)$ with small radii are not subanalytic.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-00086298
Contributor : Emmanuel Trélat <>
Submitted on : Tuesday, July 18, 2006 - 6:25:35 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Tuesday, April 6, 2010 - 12:13:56 AM

### Identifiers

• HAL Id : hal-00086298, version 1

### Citation

Emmanuel Trélat. Non subanalyticity of sub-Riemannian Martinet spheres. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2001, 332, pp.527--532. ⟨hal-00086298⟩

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