Sub-Riemannian homogeneous spaces in dimensions 3 and 4 |
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Authors: | Elisha Falbel Claudio Gorodski |
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Institution: | (1) Instituto de Matemática e Estatística, Universidade de São Paulo, caixa postal 66281, SP 05389-970 São Paulo, Brazil |
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Abstract: | Let (M,
, g) be a sub-Riemannian manifold (i.e. M is a smooth manifold,
is a smooth distribution on M and g is a smooth metric defined on
) such that the dimension of M is either 3 or 4 and
is a contact or odd-contact distribution, respectively. We construct an adapted connection on M and use it to study the equivalence problem. Furthermore, we classify the 3-dimensional sub-Riemannian manifolds which are sub-homogeneous and show the relation to Cartan's list of homogeneous CR manifolds. Finally, we classify the 4-dimensional sub-Riemannian manifolds which are sub-symmetric. |
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Keywords: | Primary 53C15 53C30 Secondary 32C16 |
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