Spherical gradient manifolds

Miebach, Christian, and Stötzel, Henrik. "Spherical gradient manifolds." Annales de l’institut Fourier 60.6 (2010): 2235-2260. <http://eudml.org/doc/116331>.

@article{Miebach2010,
abstract = {We study the action of a real-reductive group $G=K \exp (\mathfrak\{p\})$ on a real-analytic submanifold $X$ of a Kähler manifold. We suppose that the action of $G$ extends holomorphically to an action of the complexified group $G^\mathbb\{C\}$ on this Kähler manifold such that the action of a maximal compact subgroup is Hamiltonian. The moment map induces a gradient map $\mu _ \mathfrak\{p\}\colon X\rightarrow \mathfrak\{p\}$. We show that $\mu _\mathfrak\{p\}$ almost separates the $K$–orbits if and only if a minimal parabolic subgroup of $G$ has an open orbit. This generalizes Brion’s characterization of spherical Kähler manifolds with moment maps.},
affiliation = {Université de Provence Centre de Mathématiques et Informatique UMR-CNRS 6632 (LATP) 39 rue Joliot-Curie 13453 Marseille Cedex 13 (France); Ruhr-Universität Bochum Fakultät für Mathematik Universitätsstraße 150 44780 Bochum (Allemagne)},
author = {Miebach, Christian, Stötzel, Henrik},
journal = {Annales de l’institut Fourier},
keywords = {Real-reductive Lie group; Hamiltonian action; gradient map; spherical variety; real-reductive Lie group; minimal parabolic subgroup},
language = {eng},
number = {6},
pages = {2235-2260},
publisher = {Association des Annales de l’institut Fourier},
title = {Spherical gradient manifolds},
url = {http://eudml.org/doc/116331},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Miebach, Christian
AU - Stötzel, Henrik
TI - Spherical gradient manifolds
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 6
SP - 2235
EP - 2260
AB - We study the action of a real-reductive group $G=K \exp (\mathfrak{p})$ on a real-analytic submanifold $X$ of a Kähler manifold. We suppose that the action of $G$ extends holomorphically to an action of the complexified group $G^\mathbb{C}$ on this Kähler manifold such that the action of a maximal compact subgroup is Hamiltonian. The moment map induces a gradient map $\mu _ \mathfrak{p}\colon X\rightarrow \mathfrak{p}$. We show that $\mu _\mathfrak{p}$ almost separates the $K$–orbits if and only if a minimal parabolic subgroup of $G$ has an open orbit. This generalizes Brion’s characterization of spherical Kähler manifolds with moment maps.
LA - eng
KW - Real-reductive Lie group; Hamiltonian action; gradient map; spherical variety; real-reductive Lie group; minimal parabolic subgroup
UR - http://eudml.org/doc/116331
ER -