|
Fibrations and stability for compact group actions on manifolds with local bounded Ricci covering geometry
Hongzhi HUANG
Front. Math. China. 2020, 15 (1): 69-89.
https://doi.org/10.1007/s11464-020-0824-2
In the study of the collapsed manifolds with bounded sectional curvature, the following two results provide basic tools: a (singular) fibration theorem by K. Fukaya [J. Differential Geom., 1987, 25(1): 139–156] and J. Cheeger, K. Fukaya, and M. Gromov [J. Amer. Math. Soc., 1992, 5(2): 327–372], and the stability for isometric compact Lie group actions on manifolds by R. S. Palais [Bull. Amer. Math. Soc., 1961, 67(4): 362–364] and K. Grove and H. Karcher [Math. Z., 1973, 132: 11–20]. The main results in this paper (partially) generalize the two results to manifolds with local bounded Ricci covering geometry.
References |
Related Articles |
Metrics
|
15 articles
|