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- W1973607687 abstract "A helical CR structure is a decomposition of a real Euclidean space into an even-dimensional horizontal subspace and its orthogonal vertical complement, together with an almost complex structure on the horizontal space and a marked vector in the vertical space. We prove an equivalence between such structures and step-two Carnot groups equipped with a distinguished normal geodesic, and also between such structures and smooth real curves whose derivatives have constant Euclidean norm. As a consequence, we relate step-two Carnot groups equipped with sub-Riemannian geodesics with this family of curves. The restriction to the unit circle of certain planar homogeneous polynomial mappings gives an instructive class of examples. We describe these examples in detail." @default.
- W1973607687 created "2016-06-24" @default.
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- W1973607687 date "2009-03-01" @default.
- W1973607687 modified "2023-10-17" @default.
- W1973607687 title "Helical CR structures and sub-Riemannian geodesics" @default.
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- W1973607687 doi "https://doi.org/10.1080/17476930902763801" @default.
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