Cut locus of a left invariant Riemannian metric on SO3 in the axisymmetric case

JOURNAL OF GEOMETRY AND PHYSICS

卷:110

Article

Podobryaev, A. V.¹  Sachkov, Yu. L.² 

[1] Program Syst Inst RAS, Pereslavl Zalesskii, Yaroslavl Regio, Russia

[2] Univ Hradec Kralove, Fac Sci, Rokitanskeho 62, Hradec Kralove 50003, Czech Republic

关键词: Riemannian geometry;    SO3;    Sub-Riemannian geometry;    Geodesics;    Cut time;    Cut locus;   

DOI  :  10.1016/j.geomphys.2016.09.005

来源: Elsevier

【 摘 要 】

We consider a left invariant Riemannian metric on SO3 with two equal eigenvalues. We find the cut locus and the equation for the cut time. We find the diameter of such metric and describe the set of all most distant points from the identity. Also we prove that the cut locus and the cut time converge to the cut locus and the cut time in the sub-Riemannian problem on SO3 as one of the metric eigenvalues tends to infinity. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free