Geodesic
Sub-Riemannian Engel sphere
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 97-101

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The structure of the intersection of the sub-Riemannian sphere on the Engel group with a two-dimensional invariant set of discrete symmetries is described: regularity, analytic properties, exp-log category, Whitney stratification, multiplicity of points, characterization in terms of abnormal trajectories, conjugate points and Maxwell points, and explicit expressions for the sub-Riemannian distance to singular points.
Keywords: Engel group, sub-Riemannian geometry, sub-Riemannian sphere. 
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     author = {Yu. L. Sachkov and A. Yu. Popov},
     title = {Sub-Riemannian {Engel} sphere},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {97--101},
     publisher = {mathdoc},
     volume = {500},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_500_a17/}
}
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Yu. L. Sachkov; A. Yu. Popov. Sub-Riemannian Engel sphere. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 500 (2021), pp. 97-101. http://geodesic.mathdoc.fr/item/DANMA_2021_500_a17/