2005/12/13 by Weiping Yin, An Wang, Yin, Weiping +1
Mathematics · Physics and Astronomy · #32F07 #Advanced Differential Geometry Research #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary:32H15 #secondary:32F15
paper · pdf · doi:10.48550/arxiv.math/0512274
openalex publication_date 2005/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the complete invariant metrics on Cartan-Hartogs domains which are the special types of Hua domains. Firstly, we introduce a class of new complete invariant metrics on these domains, and prove that these metrics are equivalent to the Bergman metric. Secondly, the Ricci curvatures under these new metrics are bounded from above and below by the negative constants. Thirdly, we estimate the holomorphic sectional curvatures of the new metrics, we prove that the holomorphic sectional curvatures are bounded from above and below by the negative constants. Finally, by using these new metrics and Yau's Schwarz lemma we prove that the Bergman metric is equivalent to the Einstein-Kähler metric. That means the Yau's conjecture is true on Cartan-Hartogs domain.