Holland, Jonathan
(2015)
On Causal Geometries.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Causal geometries are geometric structures on manifolds for which a (non-degenerate) null cone exists at every point, such that the null cones satisfy a version of Huygen's principle. Causal geometries are a natural generalization of conformal geometries (in non-Euclidean signature). They appear naturally as incidence geometries for projective geometries in three-dimensions, and third-order ordinary differential equations. These share features with conformal geometries: null geodesics exist, as does the Weyl tensor, and there are Raychaudhuri conditions on the null geodesic deviation.
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| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
19 June 2015 |
| Date Type: |
Publication |
| Defense Date: |
20 November 2014 |
| Approval Date: |
19 June 2015 |
| Submission Date: |
28 February 2015 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
197 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
differential geometry, relativity theory, causal geometries, parabolic geometries, generalizations of Lorentzian geometry |
| Date Deposited: |
19 Jun 2015 18:24 |
| Last Modified: |
15 Nov 2016 14:26 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/24007 |
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