Wadsley, Andrew Wellard (1974) Totally geodesic foliations. PhD thesis, University of Warwick.

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Abstract

Theorem A of Chapter I states that a periodic flow on a Riemannian manifold with each trajectory geodesic is equivalent to a circle action with the same orbits. Using a similar method of proof we obtain a theorem on pointwise periodic hhomeomorphisms of immersed submanifolds. This generalises a result of N. Weaver. As an application, we show that if M is a two-dimensional Riemannian manifold with all closed geodesics then the geodesic loops of M are all of equal length.

In Chapter II, our main theorem asserts that a foliated Riemannian manifold which is foliated by totally geodesic compact leaves has finite holonomy. This result has some application to isometric immersions of Riemannian manifolds in spaces of constant curvature.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Foliations (Mathematics), Riemannian manifolds, Geometry
Official Date:	1974
Dates:	Date Event 1974 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Epstein, D. B. A.
Sponsors:	British Council
Extent:	78 leaves
Language:	eng

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