Издательство: | Книга по требованию |
Дата выхода: | июль 2011 |
ISBN: | 978-6-1312-4266-3 |
Объём: | 132 страниц |
Масса: | 221 г |
Размеры(В x Ш x Т), см: | 23 x 16 x 1 |
High Quality Content by WIKIPEDIA articles! In mathematics, an isotropic manifold is a manifold in which the geometry doesn't depend on directions. An simple example is the surface of a sphere. A homogeneous space is a similar concept. A homogeneous space can be non-isotropic (for example, a flat torus), in the sense that an invariant metric tensor on a homogeneous space may not be isotropic. In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group G is a non-empty manifold or topological space X on which G acts continuously by symmetry in a transitive way. A special case of this is when the topological group, G, in question is the homeomorphism group of the space, X. In this case X is homogeneous if intuitively X looks locally the same everywhere. Some authors insist that the action of G be effective (i.e. faithful), although the present article does not. Thus there is a group action of G on X which can be thought of as preserving some "geometric structure" on X, and making X into a single G-orbit.
Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.