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

@article{Loi2020KhlerIO,
  title={K{\"a}hler immersions of K{\"a}hler–Ricci solitons into definite or indefinite complex space forms},
  author={Andrea Loi and Roberto Mossa},
  journal={Proceedings of the American Mathematical Society},
  year={2020}
}
  • A. LoiR. Mossa
  • Published 2 March 2020
  • Mathematics
  • Proceedings of the American Mathematical Society
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 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 [3] asserting that a KRS on a compact Kähler submanifold M ⊂ CP which is a complete intersection is KE. 

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