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Journal of Lie Theory 15 (2005), No. 2, 357--377
Copyright Heldermann Verlag 2005

Multicontact Vector Fields on Hessenberg Manifolds

Alessandro Ottazzi
Mathematisches Institut, Universitšt Bern, Sidlerstrasse 5, 3012 Bern, Switzerland

In 1850, Liouville proved that any C4 conformal map between domains in R3 is necessarily the restriction of the action of one element of O(1, 4). Cowling, De Mari, Koranyi and Reimann recently proved 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.

MSC: 22E46; 53A30, 57S20

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