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Title: Totally geodesic foliations
Author: Wadsley, Andrew Wellard
ISNI:       0000 0001 3549 9217
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1974
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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.
Supervisor: Not available Sponsor: British Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics