Department of Mathematical Sciences, Ritsumeikan University Web Page

Geometry Seminar

Title : A co-dimension 3 sub-Riemannian structure on Gromoll-Meyer exotic sphere

Speaker : Kenro Furutani (Tokyo University of Science)

16:30-17:30, September 26, 2016
Room: Biwako-Kusatsu Campus (BKC), West Wing, 7th floor, 1st Laboratory of Mathematics

Abstract :
We construct a co-dimension 3 completely non-holonomic sub-bundle on the Gromoll-Meyer exotic 7 sphere based on its realization as a base space of Sp(2) principal bundle with the structure group Sp(1). The same method is valid for constructing a co-dimension 3 sub-bundle on the standard 7 sphere (and also on 4n+3 dimensional standard sphere). For the standard sphere cases a co-dimension 3 sub-bundle was constructed by making use of the Hopf bundle. Our method gives a simple proof for the standard case.