Please use this identifier to cite or link to this item:
https://hdl.handle.net/1959.11/20241
Title: | Conformal Great Circle Flows on the 3-Sphere |
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Contributor(s): | Harris, Adam (author)![]() |
Publication Date: | 2016 |
DOI: | 10.1090/proc/12819 |
Handle Link: | https://hdl.handle.net/1959.11/20241 |
Abstract: | We consider a closed orientable Riemannian 3-manifold (M,g) and a vector field X with unit norm whose integral curves are geodesics of g. Any such vector field determines naturally a 2-plane bundle contained in the kernel of the contact form of the geodesic flow of g. We study when this 2-plane bundle remains invariant under two natural almost complex structures. We also provide a geometric condition that ensures that X is the Reeb vector field of the 1-form λ obtained by contracting g with X. We apply these results to the case of great circle flows on the 3-sphere with two objectives in mind: one is to recover the result in [4] that a volume preserving great circle flow must be Hopf and the other is to characterize in a similar fashion great circle flows that are conformal relative to the almost complex structure in the kernel of λ given by rotation by π/2 according to the orientation of M. |
Publication Type: | Journal Article |
Source of Publication: | Proceedings of the American Mathematical Society, 144(4), p. 1725-1734 |
Publisher: | American Mathematical Society |
Place of Publication: | United States of America |
ISSN: | 1088-6826 0002-9939 |
Fields of Research (FoR) 2008: | 010102 Algebraic and Differential Geometry |
Fields of Research (FoR) 2020: | 490402 Algebraic and differential geometry |
Socio-Economic Objective (SEO) 2008: | 970101 Expanding Knowledge in the Mathematical Sciences |
Socio-Economic Objective (SEO) 2020: | 280118 Expanding knowledge in the mathematical sciences |
Peer Reviewed: | Yes |
HERDC Category Description: | C1 Refereed Article in a Scholarly Journal |
Appears in Collections: | Journal Article |
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