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

Yu Hang Liu

doi:10.1007/s10114-024-1418-9

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

Yu Hang Liu^*

^*Corresponding author for this work

Department of Foundational Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	3003-3026
Number of pages	24
Journal	Acta Mathematica Sinica, English Series
Volume	40
Issue number	12
DOIs	https://doi.org/10.1007/s10114-024-1418-9
Publication status	Published - Dec 2024

Keywords

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

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10.1007/s10114-024-1418-9

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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.",

keywords = "53C20, 53C21, 53C23, positive curvature, Riemannian manifolds, Six-manifolds",

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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 - https://www.scopus.com/pages/publications/85212772832

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DO - 10.1007/s10114-024-1418-9

M3 - Article

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SP - 3003

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 12

ER -

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

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