Kähler-Einstein Metrics

Key Points

• The research aims to explore Kähler-Einstein metrics through generalized complex ellipsoids.
• Introduced a formula for Kähler-Einstein metrics on the unit ball and Siegel upper half space.
• Investigated the logarithm of the defining function as a potential function for pseudometrics.
• Analyzed properties of complex ellipsoids with respect to real holomorphic vector fields.
• Demonstrated that the logarithm of the defining function yields a Kähler-Einstein pseudometric.
• Proven that complex ellipsoids possess a real holomorphic vector field with significant geometric implications.
• Provided an example of a higher order real holomorphic vector field.

Abstract