Geodesic
Hyperfoliations on compact 3-manifolds with restrictions on the external curvature of leaves
Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 651-659

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$C^\infty$-foliations of codimension 1 on compact Riemannian 3-manifolds are studied. New classes of foliations, namely hyperbolic, elliptic, and parabolic foliations, are considered. Examples of such foliations are presented. In particular, a $C^\infty$-metric of nonnegative sectional curvature on $S^3$ such that the Reeb foliation is parabolic with respect to this metric is constructed. Analytic 3-manifolds with sectional curvature of constant sign admitting parabolic foliations are classified. 
@article{MZM_1998_63_5_a1,
     author = {D. V. Bolotov},
     title = {Hyperfoliations on compact 3-manifolds with restrictions on the external curvature of leaves},
     journal = {Matemati\v{c}eskie zametki},
     pages = {651--659},
     publisher = {mathdoc},
     volume = {63},
     number = {5},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_5_a1/}
}
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D. V. Bolotov. Hyperfoliations on compact 3-manifolds with restrictions on the external curvature of leaves. Matematičeskie zametki, Tome 63 (1998) no. 5, pp. 651-659. http://geodesic.mathdoc.fr/item/MZM_1998_63_5_a1/