Fibrations of spheres by parallel great spheres and Berger's rigidity theorem

DOI10.1007/BF00140754zbMath0642.53046OpenAlexW1997516874MaRDI QIDQ1101698

Wolfgang Ziller, Herman Gluck, Frank W. Warner

Publication date: 1987

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00140754

zbMATH Keywords

cut locusHopf fibrationcurvature pinchingrigidity theoremround sphere

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Differential geometry of symmetric spaces (53C35)

Related Items

Volume-minimizing cycles in Grassmann manifolds ⋮ Substantial Riemannian submersions of \(S^{15}\) with 7-dimensional fibres ⋮ Lipschitz minimality of Hopf fibrations and Hopf vector fields ⋮ Skew Hopf fibrations ⋮ Riemannian Foliations of the Rank one Symmetric Spaces ⋮ Rigidity of the Hopf fibration ⋮ Geometry--5 ⋮ Foliations, submanifolds, and mixed curvature ⋮ A generalization of Obata's theorem ⋮ A generalization of Berger’s almost \frac{1}4-pinched manifolds theorem. I

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