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

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Wolfram Bauer
  • Kenro Furutani
  • Chisato Iwasaki

Organisationseinheiten

Externe Organisationen

  • Tokyo University of Science
  • University of Hyogo
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Details

OriginalspracheEnglisch
Seiten (von - bis)114-136
Seitenumfang23
FachzeitschriftDifferential Geometry and its Application
Jahrgang53
PublikationsstatusVeröffentlicht - 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.

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A codimension 3 sub-Riemannian structure on the Gromoll–Meyer exotic sphere. / Bauer, Wolfram; Furutani, Kenro; Iwasaki, Chisato.
in: Differential Geometry and its Application, Jahrgang 53, 08.2017, S. 114-136.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Bauer W, Furutani K, Iwasaki C. A codimension 3 sub-Riemannian structure on the Gromoll–Meyer exotic sphere. Differential Geometry and its Application. 2017 Aug;53:114-136. doi: 10.1016/j.difgeo.2017.05.010
Bauer, Wolfram ; Furutani, Kenro ; Iwasaki, Chisato. / A codimension 3 sub-Riemannian structure on the Gromoll–Meyer exotic sphere. in: Differential Geometry and its Application. 2017 ; Jahrgang 53. S. 114-136.
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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.",
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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

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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

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