Normal forms of para-CR hypersurfaces

作者：Ottazzi Alessandro^*; Schmalz Gerd

来源：Differential Geometry and its Applications, 2017, 52: 78-93.

DOI：10.1016/j.difgeo.2017.03.018

• Para-CR structures
• Chern-Moser normal form
• Multicontact structures
• Martinet distribution
• ODE symmetries

We consider hypersurfaces of finite type in a direct product space R-2 x R-2, which are analogues to real hypersurfaces of finite type in C-2. We shall consider separately the cases where such hypersurfaces are regular and singular, in a sense that corresponds to Levi degeneracy in hypersurfaces in C-2. For the regular case, we study formal normal forms and prove convergence by following Chern and Moser. The normal form of such an hypersurface, considered as the solution manifold of a 2nd order ODE, gives rise to a normal form of the corresponding 2nd order ODE. For the degenerate case, we study normal forms for weighted 1-jets. Furthermore, we study the automorphisms of finite type hypersurfaces.

• 出版日期2017-6