V-Soliton Metric with Rotationally Symmetric

In this paper, we consider the V-soliton metric on Cn and on the total space of direct sum of fixed hermitian line bundle L⊕n→M and its projective compactification P(C⊕L⊕n)=P(L-1⊕C⊕n). We prove that the V-soliton equation can be reduced to an ODE. The V-soliton metric is a solution to a degenerate fully nonlinear equation first introduced by La Nave and Tian in their study of Kähler-Ricci flow on symplectic quotients. This equation provides a framework for examining finite-time singularities of the Kähler-Ricci flow.