Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57R30

Retrieve articles in all journals with MSC: 57R30

Additional Information

PII: S 0002-9939(1979)0537106-1
Keywords: Foliations, geodesics, totally geodesic foliations, geodesibility, Reeb component
Article copyright: © Copyright 1979 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia