English

Volume comparison theorem with respect to sigma-2 curvature

Differential Geometry 2023-12-12 v2

Abstract

In this paper, we investigate the volume comparison theorem related to σ2\sigma_2-curvature. In particular, we show that volume comparison theorem with respect to σ2\sigma_2-curvature holds for metrics close to strictly stable positive Einstein metrics. By applying similar techniques, we derive the local rigidity theorem for strictly stable Ricci flat manifolds with respect to σ2\sigma_2-curvature, which shows it admits no metric with positive σ2\sigma_2-curvature near strictly stable Ricci-flat metrics.

Keywords

Cite

@article{arxiv.2111.09532,
  title  = {Volume comparison theorem with respect to sigma-2 curvature},
  author = {Jiaqi Chen and Yi Fang and Yan He and Jingyang Zhong},
  journal= {arXiv preprint arXiv:2111.09532},
  year   = {2023}
}

Comments

18 pages

R2 v1 2026-06-24T07:43:06.064Z