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SubRiemannian Geometry on the Sphere $\mathbb{S}^3$

  Published:2009-08-01
 Printed: Aug 2009
Canadian Journal of Mathematics
  • Ovidiu Calin
  • Der-Chen Chang
  • Irina Markina
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Abstract

We discuss the subRiemannian geometry induced by two noncommutative vector fields which are left invariant on the Lie group $\mathbb{S}^3$.
Keywords: noncommutative Lie group, quaternion group, subRiemannian geodesic, horizontal distribution, connectivity theorem, holonomic constraint noncommutative Lie group, quaternion group, subRiemannian geodesic, horizontal distribution, connectivity theorem, holonomic constraint
MSC Classifications: 53C17, 53C22, 35H20 show english descriptions Sub-Riemannian geometry
Geodesics [See also 58E10]
Subelliptic equations 53C17 - Sub-Riemannian geometry
53C22 - Geodesics [See also 58E10]
35H20 - Subelliptic equations
 
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