Sub-Riemannian geometry of Stiefel manifolds
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...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | 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 $V_{2k;k}$. |
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| DOI: | 10.48550/arxiv.1305.6056 |