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Rigidity of nonsteady gradient Kähler-Ricci solitons with constant scalar curvature

  • Matheus Andrade Ribeiro de Moura Horácio
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Abstract

We prove that every complete nonsteady gradient Kähler-Ricci soliton with constant scalar curvature is rigid. This establishes Cao's rigidity conjecture for Kähler-Ricci solitons in arbitrary dimension and gives the corresponding result for expanding solitons, without additional curvature assumptions. The proof uses a rigidity criterion for gradient Ricci solitons with constant scalar curvature, expressed by the vanishing of the Lie derivative of the Ricci tensor along the soliton vector field. In the Kähler case, this vanishing follows from constant scalar curvature, the closedness of the Ricci form, and the classical real holomorphicity of the soliton vector field.

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Cite

BibTeXRIS
BibTeX
@misc{horacio2026rigidity,
  title = {{Rigidity of nonsteady gradient Kähler-Ricci solitons with constant scalar curvature}},
  author = {Matheus Andrade Ribeiro de Moura Horácio},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29359},
  eprint = {2609.29359},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29359},
}
RIS
TY  - UNPB
TI  - Rigidity of nonsteady gradient Kähler-Ricci solitons with constant scalar curvature
AU  - Matheus Andrade Ribeiro de Moura Horácio
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.29359
UR  - https://arxiv.org/abs/2609.29359
AB  - We prove that every complete nonsteady gradient Kähler-Ricci soliton with constant scalar curvature is rigid. This establishes Cao's rigidity conjecture for Kähler-Ricci solitons in arbitrary dimension and gives the corresponding result for expanding solitons, without additional curvature assumptions. The proof uses a rigidity criterion for gradient Ricci solitons with constant scalar curvature, expressed by the vanishing of the Lie derivative of the Ricci tensor along the soliton vector field. In the Kähler case, this vanishing follows from constant scalar curvature, the closedness of the Ricci form, and the classical real holomorphicity of the soliton vector field.
ER  -