A codimension 3 sub-Riemannian structure on the Gromoll–Meyer exotic sphere
| Autor: | Kenro Furutani, Chisato Iwasaki, Wolfram Bauer |
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| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Group (mathematics) 010102 general mathematics Structure (category theory) Codimension 01 natural sciences Principal bundle Exotic sphere Mathematics::Algebraic Geometry Computational Theory and Mathematics Simple (abstract algebra) 0103 physical sciences Subbundle Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology 0101 mathematics Hopf fibration Analysis Mathematics |
| Zdroj: | Differential Geometry and its Applications. 53:114-136 |
| ISSN: | 0926-2245 |
| DOI: | 10.1016/j.difgeo.2017.05.010 |
| Popis: | We construct a codimension 3 completely non-holonomic subbundle on the Gromoll–Meyer exotic 7-sphere based on its realization as a base space of a Sp ( 2 ) -principal bundle with the structure group Sp ( 1 ) . The same method can be applied to construct a codimension 3 completely non-holonomic subbundle on the standard 7-sphere (or more general on a ( 4 n + 3 ) -dimensional standard sphere). In the latter case such a construction based on the Hopf bundle is well-known. Our method provides a new and simple proof for the standard sphere S 7 . |
| Databáze: | OpenAIRE |
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