Rotation invariant singular Kähler metrics with constant scalar curvature on ${\mathbb{C}}^n$

Abstract

The scalar curvature equation for rotation invariant Kähler metrics on ${\mathbb{C}}^n\backslash \{0\}$ is reduced to a system of ODEs of order 2. By solving the ODEs, we obtain complete lists of rotation invariant zero or positive csck on ${\mathbb{C}}^n\backslash \{0\}$ in lower dimensions. We also prove that there does not exist negative csck on ${\mathbb{C}}^n\backslash \{0\}$ for $n=2,3$.

arXiv comment22 pages, The definition of scalar curvature in the previous version has a wrong sign as usual. The definition and related mistakes are corrected; Some results about radial singular kähler metrics with negative constant scalar curvature is also discussed

References in corpus (3)

• On the constant scalar curvature Kähler metrics, existence results
• On the constant scalar curvature Kähler metrics, general automorphism group
• On the constant scalar curvature Kähler metrics, apriori estimates