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Solvable Lie algebras and the embedding of CR manifolds

C. Denson HillMauro Nacinovich — 1999

Bollettino dell'Unione Matematica Italiana

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.

Differential Equations and Para-CR Structures

C. Denson HillPaweł Nurowski — 2010

Bollettino dell'Unione Matematica Italiana

We study the local geometry of n dimensional manifolds which are equipped with two integrable distributions, one of dimension r and one of dimension s , where r and s are allowed to be unequal. We call them para-CR structures of type ( k , r , s ) , with k = n - r - s 0 being the para-CR codimension. When r = s they are the real analogues of CR structures. In the general case these structures are the natural geometric setting in which to discuss the geometry of systems of ODE's, as well as the geometry of systems of PDE's of finite...

The Poincaré lemma and local embeddability

Judith BrinkschulteC. Denson HillMauro Nacinovich — 2003

Bollettino dell'Unione Matematica Italiana

For pseudocomplex abstract C R manifolds, the validity of the Poincaré Lemma for 0 , 1 forms implies local embeddability in C N . The two properties are equivalent for hypersurfaces of real dimension 5 . As a corollary we obtain a criterion for the non validity of the Poicaré Lemma for 0 , 1 forms for a large class of abstract C R manifolds of C R codimension larger than one.

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