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

作　　者：Hongzhi HUANG 

机构地区：[1]School of Mathematical Sciences,Capital Normal University,Beijing 100048,China

出　　处：《Frontiers of Mathematics in China》2020年第1期69-89,共21页中国高等学校学术文摘·数学（英文）

摘　　要：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 Gcom.,1987.25(1):139156]and J.Cheeger,K.Fukaya,and M.Gromov[J.Airier.Math.Soc.,1992.5(2):327372],and the stability for isometric compact Lie group actions on manifolds by R.S.Palais[Bull.Amer.Math.Soc.,1961,67(4):362364]and K.Grove and H.Karcher[Math.Z..1973,132:1120].The main results in this paper(partially)generalize the two results to manifolds with local bounded Ricci covering geometry.

关 键 词：FIBRATIONS STABILITY for group actions nilpotent structures RICCI curvature BOUNDED RICCI COVERING GEOMETRY 

分 类 号：O152.5[理学—数学]