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Title: SUBRIEMANNIAN GEODESIC FLOW ON $mathbb{S}^7$ (Symmetry and Singularity of Geometric Structures and Differential Equations)
Author's alias: 多羅間, 大輔
Keywords: 53C17
subriemannian geometry
Poisson structure
first integrals
Issue Date: Dec-2019
Publisher: 京都大学数理解析研究所
Journal title: 数理解析研究所講究録
Volume: 2137
Start page: 42
End page: 59
Abstract: We consider three non-isometric trivializable subriemannian structures on the Euclidean 7-sphere S7 of rank 4, 5, and 6 which are induced by a Clifford module structure of R8. In this paper we explain the geometric setting and start the analysis of the corresponding subriemannian geodesic flow. We derive the geodesic flow equations and present an equivalent but more symmetric form of ODEs. In some cases we derive normal subriemannian geodesics as the projections of solutions to either of these systems and we construct some first integrals of the geodesic flow.
Appears in Collections:2137 Symmetry and Singularity of Geometric Structures and Differential Equations

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