论文信息 - (Locally) shortest arcs of special sub-Riemannian metric on the Lie group SO(3)

(Locally) shortest arcs of special sub-Riemannian metric on the Lie group SO(3)

The authors find geodesics, shortest arcs, diameter, cut locus, and conjugate sets for left-invariant sub-Riemannian metric on the Lie group SO(3), under condition that the metric is right-invariant relative to the Lie subgroup $SO(2)\subset SO(3)$.

Valera Berestovskii

[1] V. N. Berestovskĭ. Universal methods of the search of normal geodesics on Lie groups with left-invariant sub-Riemannian metric , 2014 .

[2] S. Helgason. Differential Geometry and Symmetric Spaces , 1964 .

[3] Shapes of Spheres of Special Nonholonomic Left-Invariant Intrinsic Metrics on Some Lie Groups , 2001 .

[4] L. Mirsky,et al. The Theory of Matrices , 1961, The Mathematical Gazette.

[5] W. Meyer,et al. Riemannsche Geometrie im Großen , 1975 .

[6] Shigeo Sasaki,et al. ON THE DIFFERENTIAL GEOMETRY OF TANGENT BUNDLES OF RIEMANNIAN MANIFOLDS II , 1958 .

[7] F. R. Gantmakher. The Theory of Matrices , 1984 .

[8] V. Berestovskii,et al. A Metric Characterization of Riemannian Submersions , 1999 .

[9] Francesco Rossi,et al. Invariant Carnot--Caratheodory Metrics on S3, SO(3), SL(2), and Lens Spaces , 2007, SIAM J. Control. Optim..

[10] A. Besse. Manifolds all of whose Geodesics are Closed , 2011 .