Locally convex hypersurfaces immersed in $$\mathbb {H}^n\times \mathbb {R}$$ H n × R
| Autor: | Inês S. de Oliveira Padilha, S. J. Paul A. Schweitzer |
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| Rok vydání: | 2016 |
| Předmět: |
Hyperbolic space
Hyperbolic geometry 010102 general mathematics Mathematical analysis Regular polygon Algebraic geometry 01 natural sciences Convexity Combinatorics Hypersurface Differential geometry 0103 physical sciences 010307 mathematical physics Geometry and Topology 0101 mathematics Geometry and topology Mathematics |
| Zdroj: | Geometriae Dedicata. 188:17-32 |
| ISSN: | 1572-9168 0046-5755 |
| DOI: | 10.1007/s10711-016-0202-0 |
| Popis: | We prove a theorem of Hadamard–Stoker type: a connected locally convex complete hypersurface immersed in \(\mathbb {H}^n\times \mathbb {R}\) (\(n\ge 2\)), where \(\mathbb {H}^n\) is n-dimensional hyperbolic space, is embedded and homeomorphic either to the n-sphere or to \(\mathbb {R}^n\). In the latter case it is either a vertical graph over a convex domain in \(\mathbb {H}^n\) or has what we call a simple end. |
| Databáze: | OpenAIRE |
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