关于四元数射影空间的稳定性
微分几何
2025-08-14 v1
摘要
本文旨在证明：当常四元数截面曲率 满足 时，具有该曲率的四元数空间形式上恒等映射的指标为零。作为直接推论，确立了任何具有负四元数截面曲率的紧致四元数空间形式都是稳定的，并强调相反地（但与一些已知结果一致），任何四元数射影空间都是不稳定的。
引用
@article{arxiv.2508.09315,
title = {On the stability of the quaternion projective space},
author = {Crina-Daniela Neacşu},
journal= {arXiv preprint arXiv:2508.09315},
year = {2025}
}
备注
10 pages, revised version. We have harmonized the signs of two formulas taken from different references, but which corresponded to some distinct sign conventions for the Riemannian curvature tensor. Consequently, the stability result was reformulated with the revised sign in mind