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Berestovskiĭ, V. N.; Zubareva, I. A.

Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group \(\mathrm{SL}(2)\). (English. Russian original) Zbl 1347.53028

Sib. Math. J. 57, No. 3, 411-424 (2016); translation from Sib. Mat. Zh. 57, No. 3, 527-542 (2016).
Summary: The authors found geodesics, shortest arcs, cut loci, and conjugate sets for some left-invariant sub-Riemannian metric on the Lie group \(\mathrm{SL}(2)\) that is right-invariant with respect to the Lie subgroup \(\mathrm{SO}(2)\subset\mathrm{SL}(2)\) (in other words, for invariant sub-Riemannian metrics on th weakly symmetric space \((\mathrm{SL}(2)\times\mathrm{SO}(2))/\mathrm{SO}(2))\).

Cited in 13 Documents

MSC:

53C17 Sub-Riemannian geometry
22E30 Analysis on real and complex Lie groups
53C35 Differential geometry of symmetric spaces
53C22 Geodesics in global differential geometry

Keywords:

cut locus; conjugate set; geodesic; geodesic orbit space; Lie algebra; Lie group; invariant sub-Riemannian metric; shortest arc; weakly symmetric space
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Full Text: DOI

References:

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