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01308nam a2200181Ia 4500 |
| 001 |
10.1007-s42985-022-00174-3 |
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220706s2022 CNT 000 0 und d |
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|a 26622963 (ISSN)
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| 245 |
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|a The Gauss map of minimal surfaces in S2× R
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| 260 |
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|b Springer International Publishing
|c 2022
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| 856 |
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|z View Fulltext in Publisher
|u https://doi.org/10.1007/s42985-022-00174-3
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|a In this work, we consider the model of S2×R isometric to R3\ { 0 } , endowed with a metric conformally equivalent to the Euclidean metric of R3, and we define a Gauss map for surfaces in this model likewise in the Euclidean 3-space. We show as a main result that any two minimal conformal immersions in S2×R with the same non-constant Gauss map differ by only two types of ambient isometries: either f=(Id,T), where T is a translation on R, or f= (A, T) , where A denotes the antipodal map on S2. This means that any minimal immersion is determined by its conformal structure and its Gauss map, up to those isometries. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
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|a Conformal immersions
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|a Gauss map
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|a Homogenous 3-manifolds
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| 650 |
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|a Minimal surface
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| 700 |
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|a Domingos, I.
|e author
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| 773 |
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|t Partial Differential Equations and Applications
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