Abstract
The paper studies complex manifolds whose Bergman metrics are incomplete but have constant holomorphic sectional curvature. We will construct a real analytic unbounded domain in C2 whose Bergman metric is well-defined and has a positive constant holomorphic sectional curvature, which appears to be the first example of this kind. We will answer a long standing folklore conjecture that a Stein manifold has a negative constant holomorphic sectional curvature if and only if it is biholomorphic to a ball with a pluripolar set removed. Together with the uniqueness of a moment problem in the appendix of the paper provided by John Treuer, we will show that, under natural assumptions, there is no complex manifold whose Bergman metric is flat.
| Original language | American English |
|---|---|
| Pages (from-to) | 203-220 |
| Number of pages | 18 |
| Journal | Journal fur die Reine und Angewandte Mathematik |
| Volume | 2025 |
| Issue number | 822 |
| DOIs | |
| State | Published - May 1 2025 |
| Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics