The equivalent classical metrics on the Cartan-Hartogs Domains

Details The equivalent classical metrics on the Cartan-Hartogs Domains The equivalent classical metrics on the Cartan-Hartogs Domains

2005-12-13

arxiv.org/abs/math/0512274v1

Mathematics

Complex Variables

19 pages

Scientific paper

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-K\"ahler metric. That means the Yau's conjecture is true on Cartan-Hartogs domain.

Affiliated with

Also associated with

No associations

Rating

The equivalent classical metrics on the Cartan-Hartogs Domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The equivalent classical metrics on the Cartan-Hartogs Domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The equivalent classical metrics on the Cartan-Hartogs Domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-36633