Displaying similar documents to “Lie group structures on groups of diffeomorphisms and applications to CR manifolds”

Decomposition of CR-manifolds and splitting of CR-maps

Atsushi Hayashimoto, Sung-Yeon Kim, Dmitri Zaitsev (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We show the uniqueness of local and global decompositions of abstract CR-manifolds into direct products of irreducible factors, and a splitting property for their CR-diffeomorphisms into direct products with respect to these decompositions. The assumptions on the manifolds are finite non-degeneracy and finite-type on a dense subset. In the real-analytic case, these are the standard assumptions that appear in many other questions. In the smooth case, the assumptions cannot be weakened...

The Lie group of real analytic diffeomorphisms is not real analytic

Rafael Dahmen, Alexander Schmeding (2015)

Studia Mathematica

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We construct an infinite-dimensional real analytic manifold structure on the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is defined to be real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known, the construction turns the group of real analytic diffeomorphisms into a smooth locally convex Lie group. We prove that this group is regular in the sense...

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.

Lie algebraic characterization of manifolds

Janusz Grabowski, Norbert Poncin (2004)

Open Mathematics

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Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold is characterized by the corresponding Lie algebra of linear differential operators, i.e. isomorphisms of such Lie algebras are induced by the appropriate class of diffeomorphisms of the underlying manifolds.

Solvable Lie algebras and the embedding of CR manifolds

C. Denson Hill, Mauro Nacinovich (1999)

Bollettino dell'Unione Matematica Italiana

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In questo lavoro si dà un criterio sufficiente per l'immersione di una varietà CR astratta di codimensione arbitraria in una di codimensione CR più bassa. La condizione trovata è necessaria per l'immersione in una varietà complessa (codimensione CR uguale a zero). Essa è formulata in termini dell'esistenza di una sottoalgebra di Lie di campi di vettori complessi trasversale alla distribuzione di Cauchy-Riemann.