Topology and Curvature of Isoparametric Families in Spheres  

作　　者：Chao Qian Zizhou Tang Wenjiao Yan 

机构地区：[1]School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,People’s Republic of China [2]Chern Institute of Mathematics and LPMC,Nankai University,Tianjin 300071,People’s Republic of China [3]School of Mathematical Sciences,Laboratory of Mathematics and Complex Systems,Beijing Normal University,Beijing 100875,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2023年第2期439-475,共37页数学与统计通讯（英文）

基　　金：partially supported by the NSFC(Nos.11722101,11871282,11931007);BNSF(Z190003);Nankai Zhide Foundation;Beijing Institute of Technology Research Fund Program for Young Scholars.

摘　　要：An isoparametric family in the unit sphere consists of parallel isoparametric hypersurfaces and their two focal submanifolds.The present paper has two parts.The first part investigates topology of the isoparametric families,namely the homotopy,homeomorphism,or diffeomorphism types,parallelizability,as well as the Lusternik-Schnirelmann category.This part extends substantially the results of Wang(J Differ Geom 27:55-66,1988).The second part is concerned with their curvatures;more precisely,we determine when they have non-negative sectional curvatures or positive Ricci curvatures with the induced metric.

关 键 词：Isoparametric hypersurface Focal submanifold Homotopy equivalent HOMEOMORPHISM DIFFEOMORPHISM Parallelizability Lusternik-Schnirelmann category Sectional curvature Ricci curvature 

分 类 号：O18[理学—数学]