Differential Geometry of Foliations

Author: B.L. Reinhart
Publisher: Springer Science & Business Media
ISBN: 9783642690150
Release Date: 2012-12-06
Genre: Mathematics

Whoever you are! How can I but offer you divine leaves . . . ? Walt Whitman The object of study in modern differential geometry is a manifold with a differ ential structure, and usually some additional structure as well. Thus, one is given a topological space M and a family of homeomorphisms, called coordinate sys tems, between open subsets of the space and open subsets of a real vector space V. It is supposed that where two domains overlap, the images are related by a diffeomorphism, called a coordinate transformation, between open subsets of V. M has associated with it a tangent bundle, which is a vector bundle with fiber V and group the general linear group GL(V). The additional structures that occur include Riemannian metrics, connections, complex structures, foliations, and many more. Frequently there is associated to the structure a reduction of the group of the tangent bundle to some subgroup G of GL(V). It is particularly pleasant if one can choose the coordinate systems so that the Jacobian matrices of the coordinate transformations belong to G. A reduction to G is called a G-structure, which is called integrable (or flat) if the condition on the Jacobians is satisfied. The strength of the integrability hypothesis is well-illustrated by the case of the orthogonal group On. An On-structure is given by the choice of a Riemannian metric, and therefore exists on every smooth manifold.

Books in Series

ISBN: STANFORD:36105015640415
Release Date: 1979
Genre: Monographic series

American Book Publishing Record Cumulative 1970 1974

Author: Bowker Editorial Staff
ISBN: 0835209113
Release Date: 1976

Here's quick access to more than 490,000 titles published from 1970 to 1984 arranged in Dewey sequence with sections for Adult and Juvenile Fiction. Author and Title indexes are included, and a Subject Guide correlates primary subjects with Dewey and LC classification numbers. These cumulative records are available in three separate sets.

National Union Catalog

ISBN: WISC:89015292964
Release Date: 1973
Genre: Union catalogs

Includes entries for maps and atlases.

ISBN: UOM:39015080215554
Release Date: 1974
Genre: Catalogs, Union