Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

Lines of constant geodesic curvature and the k-flows

Tools
- Tools
+ Tools

Chidley, Jon Thomas Wood (1974) Lines of constant geodesic curvature and the k-flows. PhD thesis, University of Warwick.

[img]
Preview
PDF
WRAP_Thesis_Chidley_1974.pdf - Requires a PDF viewer.

Download (51Mb) | Preview
Official URL: http://webcat.warwick.ac.uk/record=b1746491~S1

Request Changes to record.

Abstract

Much work has been done on the geodesics of a Riemannian manifold and the flow it induces on the unit tangent bundle, particularly on manifolds of negative curvature. It is the purpose of this thesis to extend this work to a more general case, considering those curves of a manifold with constant geodesic curvature •

In the first chapter we define these k-lines and develop some ideas about their geometry, contrasting and comparing them with the geodesics. We show how they give flows on T1M, develop a variational theory for them and show how matrix methods may be used to solve the variational equations.

In the second chapter we investigate a particular property, that of Anosovity, well known and documented in the geodesic case. For a particular class of k-flows we solve the matrix variation equations, giving necessary and sufficient conditions for Anosovity in terms of the geodesic normals and curvatures. On manifolds of negative curvature we assign an ‘Anosov’ number to each flow such that if it is less than zero the flow is Anosov. We end by considering families of k-flows and for a class of flows indicate the topological similarities between members of the class and in particular the geodesic flow. We end with some conjectures and ideas for future work.

Also included are two appendices. The first catalogues the results we need on the metric of the unit tangent bundle, and we extend this to the Frame bundles defining k-flows on these spaces and investigating the volume preserving properties. The second derives k-lines and flow’ from a classical mechanics point at view and justifies their study as phenomena arising from physical situations.

Item Type: Thesis (PhD)
Subjects: Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH): Riemannian manifolds, K-theory, Curvature
Official Date: 1974
Dates:
DateEvent
1974Submitted
Institution: University of Warwick
Theses Department: Mathematics Institute
Thesis Type: PhD
Publication Status: Unpublished
Supervisor(s)/Advisor: Walters, Peter, 1943-
Sponsors: Science Research Council (Great Britain)
Extent: 175 leaves
Language: eng

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us