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

Yu Hang Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)3003-3026
Number of pages24
JournalActa Mathematica Sinica, English Series
Volume40
Issue number12
DOIs
Publication statusPublished - Dec 2024

Keywords

  • 53C20
  • 53C21
  • 53C23
  • positive curvature
  • Riemannian manifolds
  • Six-manifolds

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