A codimension 3 sub-Riemannian structure on the Gromoll Meyer exotic sphere

作者：Bauer Wolfram^*; Furutani Kenro; Iwasaki Chisato

来源：Differential Geometry and its Applications, 2017, 53: 114-136.

DOI：10.1016/j.difgeo.2017.05.010

• Exotic sphere
• Non-holonomic subbundle
• Principal bundle
• Horizontal subspace

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 (4n + 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.

• 出版日期2017-8