Smooth Great Circle Fibrations and an Application to the Topological Blaschke Conjecture

DOI10.2307/2001686zbMath0704.57018OpenAlexW4235052511MaRDI QIDQ3484038

Chung-Tao Yang

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2001686

zbMATH Keywords

Hopf fibrationdiffeomorphic to \({\mathbb{C}}P^ n\)homotopy type of complex projective spacessmooth circle fibrations of round spheres and Blaschke manifolds

Mathematics Subject Classification ID

Sphere bundles and vector bundles in algebraic topology (55R25) Global Riemannian geometry, including pinching (53C20) Topology of vector bundles and fiber bundles (57R22) Differential topological aspects of diffeomorphisms (57R50)

Related Items (7)

The weak Blaschke conjecture for \(\mathbb{C} P^ n\) ⋮ Gauss maps of harmonic and minimal great circle fibrations ⋮ Skew flat fibrations ⋮ Germs of fibrations of spheres by great circles always extend to the whole sphere ⋮ Rigidity of the Hopf fibration ⋮ Geometry--5 ⋮ Foliations, submanifolds, and mixed curvature

Cites Work

• On topological Blaschke conjecture. II: Nonexistence of Blaschke structure on fake quaternion projective planes
• Division algebras, fibrations of spheres by great spheres and the topological determination of space by the gross behavior of its geodesics
• Differentiable transformation groups on homotopy spheres
• Morse Theory. (AM-51)
• Characteristic Classes. (AM-76)
• Fixed point free involutions on homotopy spheres
• Unnamed Item

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