Andrea Altomani

Holomorphic Extension from Weakly Pseudoconcave CR Manifolds

Let M be a smooth locally embeddable CR manifold, having some CR dimension m and some CR codimension d. We find an improved local geometric condition on M which guarantees, at a point p on M, that germs of CR distributions are smooth functions, and have extensions to germs of holomorphic functions on a full ambient neighborhood of p. Our condition is a form of weak pseudoconcavity, closely related to essential pseudoconcavity as introduced in [HN1]. Applications are made to CR meromorphic functions and mappings. Explicit examples are given which satisfy our new condition,but which are not pseudoconcave in the strong sense. These results demonstrate that for codimension d > 1, there are additional phenomena which are invisible when d = 1.

On the topology of minimal orbits in complex flag manifolds

We compute the Euler-Poincare characteristic of the homo- geneous compact manifolds that can be described as minimal orbits for the action of a real form in a complex flag manifold.

ON HOMOGENEOUS CR MANIFOLDS AND THEIR CR ALGEBRAS

In this paper we show some results on homogeneous CR manifolds, proved by introducing their associated CR algebras. In particular, we give different notions of nondegeneracy (generalizing the usual notion for the Levi form) which correspond to geometrical properties for the corresponding manifolds. We also give distinguished equivariant CR fibrations for homogeneous CR manifolds. In the second part of the paper we apply these results to minimal orbits for the action of a real form of a semisimple Lie group Ĝ on a flag manifold Ĝ/Q.

A Characterization of CR Quadrics with a Symmetry Property

We study CR quadrics satisfying a symmetry property

THE CR STRUCTURE OF MINIMAL ORBITS IN COMPLEX FLAG MANIFOLDS

(\tilde{S})

Classification of maximal transitive prolongations of super-Poincaré algebras

which is slightly weaker than the symmetry property (S), recently introduced by W. Kaup, which requires the existence of an automorphism reversing the gradation of the Lie algebra of infinitesimal automorphisms of the quadric.We characterize quadrics satisfying the

ORBITS OF REAL FORMS IN COMPLEX FLAG MANIFOLDS

(\tilde{S})

Tanaka structures modeled on extended Poincare algebras

property in terms of their Levi–Tanaka algebras. In many cases the

Complex vector fields and hypoelliptic partial differential operators

(\tilde{S})

REDUCTIVE COMPACT HOMOGENEOUS CR MANIFOLDS

property implies the (S) property; this holds in particular for compact quadrics.We also give a new example of a quadric such that the dimension of the algebra of positive-degree infinitesimal automorphisms is larger than the dimension of the quadric.