Antonio Lotta

A CLASSIFICATION OF SPHERICAL SYMMETRIC CR MANIFOLDS

In this paper we classify the simply connected, spherical pseudohermitian manifolds whose Webster metric is CR-symmetric.

Some Einstein nilmanifolds with skew torsion arising in CR geometry

We describe some new examples of nilmanifolds admitting an Einstein with skew torsion invariant Riemannian metric. These are affine CR quadrics, whose CR structure is preserved by the characteristic connection.

Generalized pseudohermitian manifolds

Abstract. We define a generalized pseudohermitian structure on an almost CR manifold as a pair (h,P), where h is a positive definite fiber metric h on compatible with J, and is a smooth projector such that . We show that to each generalized pseudohermitian structure one can associate a canonical linear connection on the holomorphic bundle which is invariant under equivalence. This fact allows us to solve the equivalence problem in the case where is a kind 2 distribution. We study the curvature of the canonical connection, especially for the classes of standard homogeneous manifolds and 3-Sasakian manifolds. The basic formulas for isopseudohermitian immersions are also obtained in the attempt to enlarge the theory of pseudohermitian immersions between strongly pseudoconvex pseudohermitian manifolds of hypersurface type.