Displaying similar documents to “The local equivalence problem in CR geometry”

Unique determination of local C ⁢ R -maps by their jets: a survey

Dmitri Zaitsev (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We survey results on unique determination of local C ⁢ R -automorphisms of smooth C ⁢ R -manifolds and of local biholomorphisms of real-analytic C ⁢ R -submanifolds of complex spaces by their jets of finite order at a given point. Examples generalizing [28] are given showing that the required jet order may be arbitrarily high.

On local geometry of finite multitype hypersurfaces

Martin Kolář (2007)

Archivum Mathematicum

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This paper studies local geometry of hypersurfaces of finite multitype. Catlin’s definition of multitype is applied to a general smooth hypersurface in ℂ n + 1 . We prove biholomorphic equivalence of models in dimension three and describe all biholomorphisms between such models. A finite constructive algorithm for computing multitype is described. Analogous results for decoupled hypersurfaces are given.

Parallel hypersurfaces

Barbara Opozda, Udo Simon (2014)

Annales Polonici Mathematici

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We investigate parallel hypersurfaces in the context of relative hypersurface geometry, in particular including the cases of Euclidean and Blaschke hypersurfaces. We describe the geometric relations between parallel hypersurfaces in terms of deformation operators, and we apply the results to the parallel deformation of special classes of hypersurfaces, e.g. quadrics and Weingarten hypersurfaces.