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

Abstract

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 $c$.

12 pages. To appear in Proc. Amer. Math. Soc

References in corpus (1)

• Existence of Gradient Kahler-Ricci Solitons

Cited by in corpus (8)

• Sasakian immersions of Sasaki-Ricci solitons into Sasakian space forms
• Holomorphic isometries into homogeneous bounded domains
• Submanifolds of some Hartogs domain and the complex Euclidean space
• Kaehler Ricci solitons induced by infinite dimensional complex space forms
• On holomorphic isometries into blow-ups of ${\mathbb{C}}^n$
• Umehara algebra and complex submanifolds of indefinite complex space forms
• Rigidity properties of holomorphic isometries into homogeneous Kähler manifolds
• Immersions of Sasaki-Ricci solitons into homogeneous Sasakian manifolds