Use this URL to cite or link to this record in EThOS: | http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.476184 |
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Title: | Totally geodesic foliations | ||||||
Author: | Wadsley, Andrew Wellard | ||||||
Awarding Body: | University of Warwick | ||||||
Current Institution: | University of Warwick | ||||||
Date of Award: | 1974 | ||||||
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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.
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Supervisor: | Not available | Sponsor: | British Council | ||||
Qualification Name: | Thesis (Ph.D.) | Qualification Level: | Doctoral | ||||
EThOS ID: | uk.bl.ethos.476184 | DOI: | Not available | ||||
Keywords: | QA Mathematics | ||||||
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