Kähler geometry of bounded pseudoconvex Hartogs domains

Abstract

Let $\Omega$ be a bounded pseudoconvex Hartogs domain. There exists a natural complete Kähler metric $g^{\Omega }$ in terms of its defining function. In this paper, we study two problems. The first one is determining when $g^{\Omega }$ is Einstein or extremal. The second one is the existence of holomorphic isometric immersions of $(\Omega ,g^{\Omega })$ into finite or infinite dimensional complex space forms.

Cited by in corpus (2)

• Strongly not relatives Kaehler manifolds
• Non-relativity of Kähler manifold and complex space forms