On Closed Six-Manifolds Admitting Riemannian Metrics with Positive Sectional Curvature and Non-Abelian Symmetry  

作　　者：Yu Hang LIU 

机构地区：[1]Department of Foundational Mathematics,School of Mathematics and Physics,Xi’an Jiaotong-Liverpool university,Suzhou,215123,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第12期3003-3026,共24页数学学报（英文版）

基　　金：Supported by Research Development Fund of XJTLU(Grant No.RDF-22-01-027)。

摘　　要：We study the topology of closed,simply-connected,6-dimensional Riemannian manifolds of positive sectional curvature which admit isometric actions by SU(2)or SO(3).We show that their Euler characteristic agrees with that of the known examples,i.e.,S^(6),CP^(3),the Wallach space SU(3)/T^(2)and the biquotient SU(3)/T^(2).We also classify,up to equivariant diffeomorphism,certain actions without exceptional orbits and show that there are strong restrictions on the exceptional strata.

关 键 词：Six-manifolds positive curvature Riemannian manifolds 

分 类 号：O186.12[理学—数学]