Differential Geometry of Foliations - The Fundamental Integrability Problem (Paperback, Softcover reprint of the original 1st ed. 1983)

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."

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, 99
Release date:	2012
First published:	1983
Authors:	B. L. Reinhart
Dimensions:	244 x 170 x 11mm (L x W x T)
Format:	Paperback
Pages:	196
Edition:	Softcover reprint of the original 1st ed. 1983
ISBN-13:	978-3-642-69017-4
Categories:	Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Promotions
LSN:	3-642-69017-3
Barcode:	9783642690174

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