ORCID
https://orcid.org/0000-0002-7437-5046
Abstract
In this survey paper the ultrahyperbolic equation in dimension four is discussed from a geometric, analytic and topological point of view. The geometry centres on the canonical neutral metric on the space of oriented geodesics of 3-dimensional space-forms, the analysis discusses a mean value theorem for solutions of the equation and presents a new solution of the Cauchy problem over a certain family of null hypersurfaces, while the topology relates to generalizations of codimension two foliations of 4-manifolds.
Disciplines
Geometry and Topology | Mathematics | Physical Sciences and Mathematics
DOI
10.33232/BIMS.0091.9.32
Full Publication Date
January 2023
Publisher
Irish Mathematical Society
Resource Type
journal article
Access Rights
restricted access
Open Access Route
Undetermined
Deposit Statement
© 2023 Irish Mathematical Society. Article is shared with the permission the IMS per their Copyright and Code of Submission Guidelines. The IMS grants authors of published papers free use of this pdf file; hence they may post it on personal websites or electronic archives. They may reuse the content in other publications, provided they follow academic codes of best practice as these are commonly understood.
Recommended Citation
Brendan Guilfoyle, From CT scans to 4-manifold topology via neutral geometry, Irish Math. Soc. Bulletin, Number 91, Summer 2023, 9–32, 10.33232/BIMS.0091.9.32.
Publication Details
Irish Mathematical Society Bulletin, Summer Issue 2023 9-32. © Irish Mathematical Society.