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Kähler-Ricci Shrinkers with Nonnegative Ricci Curvature
Abstract
We prove that every complete Kähler--Ricci shrinker with nonnegative Ricci curvature is holomorphically isometric to ℂk× Nn−k for some 0≤ k≤ n, where ℂk is the Gaussian shrinker and N is a compact Kähler--Ricci shrinker with nonnegative Ricci curvature. As a corollary, every complete Kähler--Ricci shrinker with quasi-positive Ricci curvature is compact.
Related
- Scalar curvature bounds and tangent cones for Kähler--Ricci shrinkers
- Kähler--Ricci Shrinkers with Constant Scalar Curvature Are Rigid
- A complete Kähler metric on ℂn of nonnegative Ricci curvature with Euclidean volume growth and nonunique asymptotic cone
- Ricci pinching on complete Kähler manifolds with nonnegative bisectional curvature
- A Matsushima theorem, uniqueness and K-polystability for Kähler-Ricci shrinkers
BibTeX
@misc{xu2026kählerricci,
title = {{Kähler-Ricci Shrinkers with Nonnegative Ricci Curvature}},
author = {Tongxin Xu and Zhenlei Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28238},
eprint = {2610.28238},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28238},
}
RIS
TY - UNPB
TI - Kähler-Ricci Shrinkers with Nonnegative Ricci Curvature
AU - Tongxin Xu
AU - Zhenlei Zhang
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28238
UR - https://arxiv.org/abs/2610.28238
AB - We prove that every complete Kähler--Ricci shrinker with nonnegative Ricci curvature is holomorphically isometric to ℂ^k× N^n−k for some 0≤ k≤ n, where ℂ^k is the Gaussian shrinker and N is a compact Kähler--Ricci shrinker with nonnegative Ricci curvature. As a corollary, every complete Kähler--Ricci shrinker with quasi-positive Ricci curvature is compact.
ER -