|
|
|||
|
||||
OverviewHigh 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. Full Product DetailsAuthor: Lambert M. Surhone , Mariam T. Tennoe , Susan F. HenssonowPublisher: VDM Publishing House Imprint: VDM Publishing House Dimensions: Width: 22.90cm , Height: 0.70cm , Length: 15.20cm Weight: 0.208kg ISBN: 9786131242663ISBN 10: 6131242666 Pages: 134 Publication Date: 14 August 2010 Audience: General/trade , General Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |