Journal of Lie Theory

no. 2
Multicontact Vector Fields on Hessenberg Manifolds
Journal of Lie Theory, Volume 15 (2005) no. 2, pp. 357-377
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.
DOI: 10.5802/jolt.380
Classification: 22E46, 53A30, 57S20
Keywords: Semisimple Lie group, contact map, conformal map, Hessenberg manifolds 
@article{JOLT_2005_15_2_a0,
     author = {A. Ottazzi},
     title = {Multicontact {Vector} {Fields} on {Hessenberg} {Manifolds}},
     journal = {Journal of Lie Theory},
     pages = {357--377},
     year = {2005},
     volume = {15},
     number = {2},
     doi = {10.5802/jolt.380},
     zbl = {1077.22019},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.380/}
}
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A. Ottazzi. Multicontact Vector Fields on Hessenberg Manifolds. Journal of Lie Theory, Volume 15 (2005) no. 2, pp. 357-377. doi: 10.5802/jolt.380

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