A differential geometric characterization of invariant domains of holomorphy

Gregor Fels

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 5, page 1329-1351
  • ISSN: 0373-0956

Abstract

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Let G = K ℂ be a complex reductive group. We give a description both of domains Ω ⊂ G and plurisubharmonic functions, which are invariant by the compact group, K , acting on G by (right) translation. This is done in terms of curvature of the associated Riemannian symmetric space M : = G / K . Such an invariant domain Ω with a smooth boundary is Stein if and only if the corresponding domain Ω M ⊂ M is geodesically convex and the sectional curvature of its boundary S : = ∂ Ω M fulfills the condition K S ( E ) ≥ K M ( E ) + k ( E , n ) . The term k ( E , n ) is explicitly computable and depends only on the normal vector n and the two dimensional tangent plane E .

How to cite

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Fels, Gregor. "A differential geometric characterization of invariant domains of holomorphy." Annales de l'institut Fourier 45.5 (1995): 1329-1351. <http://eudml.org/doc/75162>.

@article{Fels1995,
abstract = {Let $G=K^\{\Bbb C\}$ be a complex reductive group. We give a description both of domains $\Omega \subset G$ and plurisubharmonic functions, which are invariant by the compact group, $K$, acting on $G$ by (right) translation. This is done in terms of curvature of the associated Riemannian symmetric space $M:=G/K$. Such an invariant domain $\Omega $ with a smooth boundary is Stein if and only if the corresponding domain $\Omega _M\subset M$ is geodesically convex and the sectional curvature of its boundary $S:=\partial \Omega _M$ fulfills the condition $K^S(E)\ge K^M(E)+k(E,n) $. The term $k(E,n)$ is explicitly computable and depends only on the normal vector $n$ and the two dimensional tangent plane $E$.},
author = {Fels, Gregor},
journal = {Annales de l'institut Fourier},
keywords = {complex Lie group; plurisubharmonic function; Riemannian symmetric space; Stein domain},
language = {eng},
number = {5},
pages = {1329-1351},
publisher = {Association des Annales de l'Institut Fourier},
title = {A differential geometric characterization of invariant domains of holomorphy},
url = {http://eudml.org/doc/75162},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Fels, Gregor
TI - A differential geometric characterization of invariant domains of holomorphy
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 5
SP - 1329
EP - 1351
AB - Let $G=K^{\Bbb C}$ be a complex reductive group. We give a description both of domains $\Omega \subset G$ and plurisubharmonic functions, which are invariant by the compact group, $K$, acting on $G$ by (right) translation. This is done in terms of curvature of the associated Riemannian symmetric space $M:=G/K$. Such an invariant domain $\Omega $ with a smooth boundary is Stein if and only if the corresponding domain $\Omega _M\subset M$ is geodesically convex and the sectional curvature of its boundary $S:=\partial \Omega _M$ fulfills the condition $K^S(E)\ge K^M(E)+k(E,n) $. The term $k(E,n)$ is explicitly computable and depends only on the normal vector $n$ and the two dimensional tangent plane $E$.
LA - eng
KW - complex Lie group; plurisubharmonic function; Riemannian symmetric space; Stein domain
UR - http://eudml.org/doc/75162
ER -

References

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