On the Szegö kernel of Cartan-Hartogs domains

Abstract

Inspired by the work of Z. Lu and G. Tian [21] in the compact setting, in this paper we address the problem of studying the Szegö kernel of the disk bundle over a noncompact Kähler manifold. In particular we compute the Szegö kernel of the disk bundle over a Cartan-Hartogs domain based on a bounded symmetric domain. The main ingredients in our analysis are the fact that every Cartan-Hartogs domain can be viewed as an "iterated" disk bundle over its base and the the ideas given in [4] for the computation of the Szegö kernel of the disk bundle over an Herimitian symmetric space of compact type.

11 pp

References in corpus (4)

• Kaehler-Einstein submanifolds of the infinite dimensional projective space
• Balanced metrics on Cartan and Cartan-Hartogs domains
• On canonical metrics on Cartan-Hartogs domains
• Canonical metrics on Cartan--Hartogs domains