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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Totally geodesic foliations on $ 3$-manifolds


Authors: David L. Johnson and Lee B. Whitt
Journal: Proc. Amer. Math. Soc. 76 (1979), 355-357
MSC: Primary 57R30
MathSciNet review: 537106
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Abstract: If M is a compact 3-manifold, it is known that M can be foliated by 2-manifolds. Topological obstructions are given to the geodesibility of such a foliation $ \mathcal{F}$; that is, to the existence of a Riemannian metric on M making each leaf a totally geodesic submanifold. For example, $ {\pi _1}(M)$ must be infinite, and hence the Reeb foliation of $ {S^3}$ is not geodesible.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0537106-1
PII: S 0002-9939(1979)0537106-1
Keywords: Foliations, geodesics, totally geodesic foliations, geodesibility, Reeb component
Article copyright: © Copyright 1979 American Mathematical Society