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Математика

Основы математического анализа и элементы дифференциальных уравнений

Наименование:

Sub-Riemannian Manifold

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мягкая обложка
100 страниц
2010 год

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Книга по Требованию

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In mathematics, a sub-Riemannian manifold is a certain type of generalization of a Riemannian manifold. Geometric quantities such as the Berry phase may be understood in the language of sub-Riemannian geometry. The Heisenberg group, important to quantum mechanics, carries a natural sub-Riemannian structure. The Hausdorff dimension of such metric spaces is always an integer and larger than its topological dimension (unless it is actually a Riemannian manifold). Sub-Riemannian manifolds often occur in the study of constrained systems in classical mechanics, such as the motion of vehicles on a surface, the motion of robot arms, and the orbital dynamics of satellites. High Quality Content by WIKIPEDIA articles! Roughly speaking, to measure distances in a sub-Riemannian manifold, you are allowed to go only along curves tangent to so-called horizontal subspaces. Sub-Riemannian manifolds (and so, a fortiori, Riemannian manifolds) carry a natural intrinsic metric called the metric of Carnot–Caratheodory.

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Sub-Riemannian Manifold Lambert M. S. http://www.booksiti.net.ru/books/17127650

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