Multicontact Vector Fields on Hessenberg Manifolds

Alessandro Ottazzi

Abstract: In 1850, Liouville proved that any $C^4$ conformal map between domains in $\R^3$ is necessarily the restriction of the action of one element of O$(1,4)$. Cowling, De Mari, Koranyi and Reimann recently prove a Liouville-type result: they defined a generalized contact structure on homogeneous spaces of the type G/P, where G is a semisimple Lie group and P a minimal parabolic subgroup, and they show that the group of "contact" mappings coincides with G. In this paper, we consider the problem of characterizing the "contact" mappings on a natural class of submanifolds of G/P, namely the Hessenberg manifolds.

Keywords: semisimple Lie group, contact map, conformal map, Hessenberg manifolds

Classification (MSC2000): 22E46, 53A30, 57S20

Full text of the article: (for faster download, first choose a mirror)

• PDF file (256 kilobytes)