منابع مشابه
Extremal Curves in Nilpotent Lie Groups
We classify extremal curves in free nilpotent Lie groups. The classification is obtained via an explicit integration of the adjoint equation in Pontryagin Maximum Principle. It turns out that abnormal extremals are precisely the horizontal curves contained in algebraic varieties of a specific type. We also extend the results to the nonfree case.
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In this paper, we study inextensible ows in three dimensional Lie groups with a bi-invariant metric. The necessary and sucient conditions for inextensible curve ow are expressed as a partial dierential equation involving the curvatures. Also, we give some results for special cases of Lie groups.
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Colloq. Algebraic Topology, 1962, pp. 104-113, Matematisk Institut, Aarhus Universitet, Denmark. 4. M. F. Atiyah, Thorn complexes, Proc. London Math. Soc. (3) 11 (1961), 291310. 5. M. F. Atiyah and J. A. Todd, On complex Stiefel manifolds, Proc. Cambridge Philos. Soc. 56 (1960), 342-353. 6. Sze-Tsen Hu, Homotopy theory, Pure and Applied Mathematics VIII, Academic Press, New York and London, 195...
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We generalize a result of Tao which describes approximate multiplicative groups in the Heisenberg group. We extend it to simply connected nilpotent Lie groups of arbitrary step.
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2013
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-013-0226-7