PreprintCC BY 4.0arXiv
Extremal Kähler--Ricci solitons on Fano manifolds are Kähler--Einstein
Abstract
We prove that every extremal Kähler--Ricci soliton on a Fano manifold is Kähler--Einstein. This solves the problem of Calamai and Petrecca in full generality.
Related
- Finite-Time Singularities of the Kähler--Ricci Flow on a ℂPm-Bundle over a Product of Kähler--Einstein Manifolds
- Shrinking Kähler-Ricci solitons on toric fano fibrations
- Linear Stability of Steady and Expanding Kähler-Ricci Solitons
- Kählerity of complete almost-Kähler gradient shrinking Ricci solitons
- Rigidity of nonsteady gradient Kähler-Ricci solitons with constant scalar curvature
BibTeX
@misc{nitta2026extremal,
title = {{Extremal Kähler--Ricci solitons on Fano manifolds are Kähler--Einstein}},
author = {Yasufumi Nitta},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23630},
eprint = {2609.23630},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23630},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Extremal Kähler--Ricci solitons on Fano manifolds are Kähler--Einstein
AU - Yasufumi Nitta
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23630
UR - https://arxiv.org/abs/2609.23630
AB - We prove that every extremal Kähler--Ricci soliton on a Fano manifold is Kähler--Einstein. This solves the problem of Calamai and Petrecca in full generality.
ER -