Gromoll, Detlef; Grove, Karsten One-dimensional metric foliations in constant curvature spaces. (English) Zbl 0566.53035 Differential geometry and complex analysis, Vol. dedic. H. E. Rauch, 165-168 (1985). [For the entire collection see Zbl 0561.00010.] The structure of one-dimensional bundle-like foliations of spaces of constant curvature are investigated in relation to the curvature and integrability tensors of Riemannian submersions. A corollary of the main result is that the only foliations of Euclidean spheres of that kind are the Hopf fibrations. Reviewer: J.Hebda Cited in 3 ReviewsCited in 14 Documents MSC: 53C12 Foliations (differential geometric aspects) 57R30 Foliations in differential topology; geometric theory 53C20 Global Riemannian geometry, including pinching Keywords:bundle-like foliations; constant curvature; Riemannian submersions; Hopf fibrations Citations:Zbl 0561.00010 PDFBibTeX XML