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arXiv · 2210.12323

Bergman-Einstein metrics on two-dimensional Stein spaces

Soumya Ganguly·Shubham Sinha
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Abstract

We show that the Bergman metric of the ball quotients $\mathbb{B}^2/\Gamma$, where $\Gamma$ is a finite and fixed point free group, is K\"ahler-Einstein if and only if $\Gamma$ is trivial. As a consequence, we characterize the unit ball $\mathbb{B}^2$, among 2 dimensional Stein spaces with isolated normal singularities, proving an algebraic version of Cheng's conjecture for 2 dimensional Stein spaces.

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Soumya Ganguly, Shubham Sinha. 2022-10-22. Bergman-Einstein metrics on two-dimensional Stein spaces. https://arxiv.org/abs/2210.12323

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