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 ⊂ CPN which is a complete intersection is Kähler-Einstein (KE).

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

Loi A.;Mossa R.
2021-01-01

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 ⊂ CPN which is a complete intersection is Kähler-Einstein (KE).
2021
Calabi's diastasis function
Complex space forms
Kähler metrics
Kähler-Einstein metrics
Kähler-Ricci solitons
Calabi's diastasis function; complex space forms; Kähler metrics; Kähler-Einstein metrics; Kähler-Ricci solitons
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[18] A. Loi, R. Mossa, Proc. Amer. Math. Soc. 149 (2021), no. 11, 4931-4941.pdf

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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/319008
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