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On Causal Geometries

Holland, Jonathan (2015) On Causal Geometries. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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Status: Unpublished
CreatorsEmailPitt UsernameORCID
Holland, Jonathanjeh89@pitt.eduJEH89
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairSparling, Georgesparling@pitt.eduSPARLING
Committee MemberHales, Thomashales@pitt.eduHALES
Committee MemberIon, Bogdanbion@pitt.eduBION
Committee MemberSati, Hishamhsati@pitt.eduHSATI
Committee MemberDunajski,
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


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