Curvilinear coordinates on generic conformally flat hypersurfaces and constant curvature 2-metrics
| Autor: | Burstall, Francis E., Hertrich-Jeromin, Udo, Suyama, Yoshihiko |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Journal of the Mathematical Society of Japan. 70, 2, (2018) 617-649 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2969/jmsj/07027420 |
| Popis: | There is a one-to-one correspondence between associated families of generic conformally flat (local-)hypersurfaces in 4-dimensional space forms and conformally flat 3-metrics with the Guichard condition. In this paper, we study the space of conformally flat 3-metrics with the Guichard condition: for a conformally flat 3-metric with the Guichard condition in the interior of the space, an evolution of orthogonal (local-) Riemannian $2$-metrics with constant Gauss curvature $-1$ is determined; for a $2$-metric belonging to a certain class of orthogonal analytic $2$-metrics with constant Gauss curvature $-1$, a one-parameter family of conformally flat 3-metrics with the Guichard condition is determined as evolutions issuing from the $2$-metric. Comment: 31 pages. v2: acknowledgement of support added; metadata corrected. v3: minor changes after referee's report |
| Databáze: | arXiv |
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