Curvature pinching estimate under the Laplacian G_{2} flow
Differential Geometry
2023-08-01 v2
Abstract
In this paper, we derive a pinching estimate on the traceless Ricci curvature in term of scalar curvature and the C^{1} norm of the Weyl tensor under the Laplacian G_{2} flow for closed G_{2} structures. Then we apply this estimate to study the long time existence of the Laplacian G_{2} flow and prove that the C^{1} norm of the Weyl tensor has to blow up at least at a certain rate under bounded scalar curvature.
Keywords
Cite
@article{arxiv.2307.14289,
title = {Curvature pinching estimate under the Laplacian G_{2} flow},
author = {Chuanhuan Li and Yi Li},
journal= {arXiv preprint arXiv:2307.14289},
year = {2023}
}
Comments
23 pages, updated version