具有非负截面曲率的 $S^2\times S^2$ 非线性对合轨道空间
微分几何
2018-12-14 v3
摘要
我们描述了一种在闭光滑不可定向4-流形上构造具有非负截面曲率的黎曼度量的方法，该流形基本群阶为2，并实现了一个同伦类，该类先前未知包含非负曲率流形。该过程在以2-球面或实射影平面为底空间的任意2-球面丛上给出了新的非负截面曲率度量。
引用
@article{arxiv.1506.01578,
title = {An orbit space of a nonlinear involution of $S^2\times S^2$ with nonnegative sectional curvature},
author = {Rafael Torres},
journal= {arXiv preprint arXiv:1506.01578},
year = {2018}
}
备注
v3: Renato Bettiol kindly pointed out to us a mistake in v2: the gluing diffeomorphism was NOT an isometry of the chosen metrics on the disk bundles. This version corrects the mistake. New title reflects that the paper has been completely rewritten having only the four-dimensional scenario as a case study