Fibrations and stability for compact group actions on manifolds with local bounded Ricci covering geometry

doi:10.1007/s11464-020-0824-2

Front. Math. China

2020, Vol. 15

Issue (1) : 69-89 https://doi.org/10.1007/s11464-020-0824-2

RESEARCH ARTICLE

Fibrations and stability for compact group actions on manifolds with local bounded Ricci covering geometry

Hongzhi HUANG(

)

School of Mathematical Sciences, Capital Normal University, Beijing 100048, China

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Abstract

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.

Keywords Fibrations stability for group actions nilpotent structures Ricci curvature bounded Ricci covering geometry

Corresponding Author(s): Hongzhi HUANG

Issue Date: 09 March 2020

Cite this article:

Hongzhi HUANG. Fibrations and stability for compact group actions on manifolds with local bounded Ricci covering geometry[J]. Front. Math. China, 2020, 15(1): 69-89.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0824-2
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I1/69

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