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

The scalar curvature equation for rotation invariant Kahler 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 $n=2,3$.