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Cylindricity of Isometric Immersions between Hyperbolic Spaces
| Content Provider | Scilit |
|---|---|
| Author | Alexander, S. Portnoy, E. |
| Copyright Year | 1978 |
| Description | The motivation for this paper was to prove the following analogue of the Euclidean cylinder theorem: any umbilic-free isometric immersion between hyperbolic spaces takes the form of a hyperbolic -cylinder over a uniquely determined parallelizing curve in . Our approach is through the more general study of isometric immersions generated by one-parameter families of hyperbolic k-planes without focal points. A by-product of this study is a natural extension to curves in of the notion of a parallel family of k-planes along a curve in ; the extension is based on spherical symmetry of variation fields. Existence and uniqueness properties of this extended notion of parallelism are considered. |
| Related Links | https://www.ams.org/tran/1978-237-00/S0002-9947-1978-0461379-0/S0002-9947-1978-0461379-0.pdf |
| Ending Page | 329 |
| Page Count | 19 |
| Starting Page | 311 |
| ISSN | 00029947 |
| e-ISSN | 10886850 |
| DOI | 10.2307/1997624 |
| Journal | Transactions of the American Mathematical Society |
| Volume Number | 237 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1978-03-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Physics Hyperbolic Isometric Immersion Cylinder Theorem Cylindricity Symmetry Motivation Eta Takes |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
