On 2-Convex Non-Orientable Surfaces in Four-Dimensional Euclidean Space
We prove that a 2-convex closed surface $S\subset E^4$ in the four-dimensional Euclidean space $E^4$, which is either $C^2$-smooth or polyhedral, provided that each vertex is incident to at most five edges, admits a mapping of degree one to a two-dimensional torus, where the degree is assumed to be$...
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| Date: | 2025 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2025
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| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1113 |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Summary: | We prove that a 2-convex closed surface $S\subset E^4$ in the four-dimensional Euclidean space $E^4$, which is either $C^2$-smooth or polyhedral, provided that each vertex is incident to at most five edges, admits a mapping of degree one to a two-dimensional torus, where the degree is assumed to be$\mod 2$ if $S$ is non-orientable. As a corollary, we show that the projective plane and the Klein bottle do not admit such a 2-convex embedding in $E^4$.
Mathematical Subject Classification 2020: 53A05, 57R19 |
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