zbMATH — the first resource for mathematics

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

53C12 Foliations (differential geometric aspects)
57R30 Foliations in differential topology; geometric theory
53C20 Global Riemannian geometry, including pinching