descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2014Embargo end date: 01 Jan 2013 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Control and Optimization, volume 52, pages 939-959 (issn: 0363-0129, eissn: 1095-7138,

Authors: Christian Autenried; Irina Markina;

doi: 10.1137/130922537 , 10.48550/arxiv.1305.6056

arXiv: http://arxiv.org/abs/1305.6056

Sub-Riemannian Geometry of Stiefel Manifolds

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Abstract

In the paper we consider the Stiefel manifold $V_{n;k}$ as a principal $U(k)$- bundle over the Grassmann manifold and study the cut locus from the unit element. We gave the complete description of this cut locus on $V_{n;1}$ and presented the sufficient condition on the general case. At the end, we study the complement to the cut locus of $V_{2k;k}$.

Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), Optimization and Control (math.OC), FOS: Mathematics, Mathematics - Optimization and Control

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