Kähler immersions of Kähler-Ricci solitons into definite or indefinite complex space forms

英文摘要：

Let $(g, X)$ be a Kähler-Ricci soliton on a complex manifold $M$. We prove that if the Kähler manifold $(M, g)$ can be Kähler immersed into a definite or indefinite complex space form of constant holomorphic sectional curvature $2c$, then $g$ is Einstein. Moreover, its Einstein constant is a rational multiple of $c$.