Rank two fundamental groups of positively curved manifolds

DOI10.1007/BF02921991zbMath0980.57017OpenAlexW3021833325MaRDI QIDQ5950227

Karsten Grove, Krishnan Shankar

Publication date: 5 March 2002

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02921991

zbMATH Keywords

torus actionsfinite group actionspositive curvature

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Compact Lie groups of differentiable transformations (57S15) Homotopy groups of topological groups and homogeneous spaces (57T20)

Related Items (7)

A panoramic glimpse of manifolds with sectional curvature bounded from below ⋮ Positively curved Riemannian metrics with logarithmic symmetry rank bounds ⋮ Revisiting homogeneous spaces with positive curvature ⋮ Fundamental groups of manifolds with positive sectional curvature and torus symmetry ⋮ Isometry groups of homogeneous spaces with positive sectional curvature ⋮ A minimal Brieskorn 5-sphere in the Gromoll-Meyer sphere and its applications ⋮ Obstructions to free actions on Bazaikin spaces

Cites Work

• On isotropy irreducible Riemannian manifolds
• Sous-groupes commutatifs et torsion des groupes de Lie compacts connexes
• New examples of manifolds with strictly positive curvature
• On the fundamental groups of positively curved manifolds
• Cohomogeneity one manifolds with positive Ricci curvature
• The almost cyclicity of the fundamental groups of positively curved manifolds
• An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures
• The normal homogeneous space (𝖲𝖴(3)×𝖲𝖮(3))/𝖴^{∙}(2) has positive sectional curvature
• Isometry groups of homogeneous spaces with positive sectional curvature
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