TY - JOUR
T1 - On Closed Six-Manifolds Admitting Riemannian Metrics with Positive Sectional Curvature and Non-Abelian Symmetry
AU - Liu, Yu Hang
N1 - Publisher Copyright:
© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2024.
PY - 2024/12
Y1 - 2024/12
N2 - 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., S6, CP3, the Wallach space SU(3)/T2 and the biquotient SU(3)//T2. We also classify, up to equivariant diffeomorphism, certain actions without exceptional orbits and show that there are strong restrictions on the exceptional strata.
AB - 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., S6, CP3, the Wallach space SU(3)/T2 and the biquotient SU(3)//T2. We also classify, up to equivariant diffeomorphism, certain actions without exceptional orbits and show that there are strong restrictions on the exceptional strata.
KW - 53C20
KW - 53C21
KW - 53C23
KW - positive curvature
KW - Riemannian manifolds
KW - Six-manifolds
UR - http://www.scopus.com/inward/record.url?scp=85212772832&partnerID=8YFLogxK
U2 - 10.1007/s10114-024-1418-9
DO - 10.1007/s10114-024-1418-9
M3 - Article
AN - SCOPUS:85212772832
SN - 1439-8516
VL - 40
SP - 3003
EP - 3026
JO - Acta Mathematica Sinica, English Series
JF - Acta Mathematica Sinica, English Series
IS - 12
ER -