On rotationally symmetric Kähler-Ricci solitons

In this note, using Calabi’s method, we construct rotationally symmetric KählerRicci solitons on the total space of direct sum of fixed hermitian line bundle and its projective compactification, where the curvature of hermitian line bundle is Kähler-Einstein. These examples generalize the construction of Koiso, Cao and Feldman-Ilmanen-Knopf. 1 A little motivation In [1], the authors constructed some examples of gradient Kähler-Ricci soliton. Among them is the shrinking soliton on the Bl0C . They also glue this to an expanding soliton on C to extend the Ricci flow across singular time. Recently, La Nave and Tian [7] studied the formation of singularity along Kähler-Ricci flow by symplectic quotient. The idea is explained by the following example. Let C∗ act on C by t · (x1, · · · , xm, y1, · · · , yn) = (t x1, · · · , t xm, t−1 y1, · · · , t−1 yn) S ⊂ C∗ preserves the standard Kähler structure on C: ω = √ −1( m