EUDML

Given the notion of $C R$ -structures without torsion on a real $2 n + 1$ dimensional Lie algebra $L_{0}$ we study the problem of their classification when $L_{0}$ is a reductive algebra.

Levi-equation in higher dimensions

Zbginiew Slodkowski; Giuseppe Tomassini — 1991

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

We announce some results concerning the Dirichlet problem for the Levi-equation in $C^{n}$ . We consider for the sake of simplicity the case $n = 3$ .

Transversally Pseudoconvex Foliations

Giuseppe Tomassini; Sergio Venturini — 2010

Bollettino dell'Unione Matematica Italiana

We consider real analytic foliations $X$ with complex leaves of transversal dimension one and we give the notion of transversal pseudoconvexity. This amounts to require that the transverse bundle $N_{F}$ to the leaves carries a metric $\{\lambda_{j}\}$ on the the fibres such that the tangential (1,1)-form $\Omega=\{\lambda_{j}\bar{\partial}\partial\lambda_{j}-2\bar{\partial}\lambda_{% j}\partial\lambda_{j}\}$ is positive. This condition is of a special interest if the foliation $X$ is 1 complete i.e. admits a smooth exhaustion function $\phi$ which is strongly plusubharmonic along the leaves. In this situation we prove that there...

Levi equation and evolution of subsets of $C^{2}$

Zbigniew Slodkowski; Giuseppe Tomassini — 1996

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

In this Note we state some results obtained studying the evolution of compact subsets of $C^{2}$ by Levi curvature. This notion appears to be the natural extension to Complex Analysis of the notion of evolution by mean curvature.

Géométrisation des modifications formelles

Vincenzo Ancona; Giuseppe Tomassini — 1978

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

Si dimostra la versione analitica dei teoremi di M. Artin sull'esistenza delle modificazioni nella categoria degli spazi algebrici (cfr. [2]).

Foliations with complex leaves

Giuliana Gigante; Giuseppe Tomassini — 1993

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

Let $X$ be a smooth foliation with complex leaves and let $D$ be the sheaf of germs of smooth functions, holomorphic along the leaves. We study the ringed space $(X, D)$ . In particular we concentrate on the following two themes: function theory for the algebra $D (X)$ and cohomology with values in $D$ .