Geometric norm equality related to the harmonicity of the Poisson kernel for homogeneous Siegel domains

摘要

In this paper, we present a geometric norm equality involving an admissible linear form omega for the Shilov boundary of a homogeneous Siegel domain D. We prove that the validity of this norm equality is equivalent to the symmetry of D and the reduction of 0) essentially to the Koszul form. This, in particular, reveals a geometric reason that the Poisson kernel is annihilated by the Laplace-Beltrami operator if and only if D is symmetric, a theorem due to Hua, Look, Koranyi and Xu. (C) 2002 Elsevier Science (USA). All rights reserved. [References: 35]