When is the Carathéodory metric a Kähler metric?
Abstract
We prove that if the Carathéodory metric on a strictly pseudoconvex domain with a smooth boundary is a Kähler metric, then the domain is biholomorphic to a ball. Additionally, we highlight the relationships between the Lu constant and the holomorphic Bergman curvature.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.09572
- arXiv:
- arXiv:2408.09572
- Bibcode:
- 2024arXiv240809572D
- Keywords:
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- Mathematics - Complex Variables;
- Mathematics - Differential Geometry;
- Primary 32F45;
- Secondary 32T15;
- 32H02
- E-Print:
- 14 pages