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

Loi, Andrea; Mossa, Roberto

doi:10.1090/proc/15628

Kähler immersions of Kähler–Ricci solitons into definite or indefinite complex space forms
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by Andrea Loi and Roberto Mossa PDF

Proc. Amer. Math. Soc. 149 (2021), 4931-4941

Abstract:

Let $(g, X)$ be a Kähler–Ricci soliton (KRS) 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 then $g$ is Einstein. Notice that there is no topological assumptions on the manifold $M$ and the Kähler immersion is not required to be injective. Our result extends the result obtained in Bedulli and Gori [Proc. Amer. Math. Soc. 142 (2014), pp. 1777–1781] asserting that a KRS on a compact Kähler submanifold $M\subset \mathbb {C}\mathrm {P}^N$ which is a complete intersection is Kähler-Einstein (KE).

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