Details
| Original language | English |
|---|---|
| Pages (from-to) | 114-136 |
| Number of pages | 23 |
| Journal | Differential Geometry and its Application |
| Volume | 53 |
| Publication status | Published - Aug 2017 |
Abstract
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 S7.
Keywords
- Exotic sphere, Horizontal subspace, Non-holonomic subbundle, Principal bundle
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Geometry and Topology
- Computer Science(all)
- Computational Theory and Mathematics
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In: Differential Geometry and its Application, Vol. 53, 08.2017, p. 114-136.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A codimension 3 sub-Riemannian structure on the Gromoll–Meyer exotic sphere
AU - Bauer, Wolfram
AU - Furutani, Kenro
AU - Iwasaki, Chisato
N1 - Funding Information: The first named author acknowledges support through the DFG project (BA 3793/6-1) in the framework of the SPP Geometry at infinity. The second named author was supported by the Grant-in-aid for Scientific Research (C) No. 26400124, JSPS and the National Center for Theoretical Science, National Taiwan University, Taiwan (Grant 105-2119-M-002-019). The third named author was supported by the National Center for Theoretical Science, National Taiwan University, Taiwan. Publisher Copyright: © 2017 Elsevier B.V. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/8
Y1 - 2017/8
N2 - 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 S7.
AB - 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 S7.
KW - Exotic sphere
KW - Horizontal subspace
KW - Non-holonomic subbundle
KW - Principal bundle
UR - http://www.scopus.com/inward/record.url?scp=85020429025&partnerID=8YFLogxK
U2 - 10.1016/j.difgeo.2017.05.010
DO - 10.1016/j.difgeo.2017.05.010
M3 - Article
AN - SCOPUS:85020429025
VL - 53
SP - 114
EP - 136
JO - Differential Geometry and its Application
JF - Differential Geometry and its Application
SN - 0926-2245
ER -