Normal forms of para-CR hypersurfaces

2016/11/22 by Alessandro Ottazzi, Ottazzi, Alessandro, Gerd Schmalz +1
Mathematics · #22E46 #32V99 #34A26 #53D10 #58D19 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1611.07576

openalex publication_date 2016/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider hypersurfaces of finite type in a direct product space \mathbb R² × \mathbb R², which are analogues to real hypersurfaces of finite type in \mathbb C². We shall consider separately the cases where such hypersurfaces are regular and singular, in a sense that corresponds to Levi degeneracy in hypersurfaces in \mathbb C². 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 ℓ-jets. Furthermore, we study the automorphisms of finite type hypersurfaces.

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