عنوان

Riemannian Foliations

شابک

9781468486704

شابک

9781468486728

شماره

b403719

عنوان اصلي

Riemannian Foliations

نام عام مواد

[Book]

نام نخستين پديدآور

by Pierre Molino.

محل نشرو پخش و غیره

Boston, MA :

نام ناشر، پخش کننده و غيره

Birkhäuser Boston,

تاریخ نشرو بخش و غیره

1988.

عنوان فروست

Progress in Mathematics ;

مشخصه جلد

73

متن يادداشت

1 Elements of Foliation theory -- 1.1. Foliated atlases ; foliations -- 1.2. Distributions and foliations -- 1.3. The leaves of a foliation -- 1.4. Particular cases and elementary examples -- 1.5. The space of leaves and the saturated topology -- 1.6. Transverse submanifolds ; proper leaves and closed leaves -- 1.7. Leaf holonomy -- 1.8. Exercises -- 2 Transverse Geometry -- 2.1. Basic functions -- 2.2. Foliate vector fields and transverse fields -- 2.3. Basic forms -- 2.4. The transverse frame bundle -- 2.5. Transverse connections and G-structures -- 2.6. Foliated bundles and projectable connections -- 2.7. Transverse equivalence of foliations -- 2.8. Exercises -- 3 Basic Properties of Riemannian Foliations -- 3.1. Elements of Riemannian geometry -- 3.2. Riemannian foliations: bundle-like metrics -- 3.3. The Transverse Levi-Civita connection and the associated transverse parallelism -- 3.4. Properties of geodesics for bundle-like metrics -- 3.5. The case of compact manifolds : the universal covering of the leaves -- 3.6. Riemannian foliations with compact leaves and Satake manifolds -- 3.7. Riemannian foliations defined by suspension -- 3.8. Exercises -- 4 Transversally Parallelizable Foliations -- 4.1. The basic fibration -- 4.2. CompIete Lie foliations -- 4.3. The structure of transversally parallelizable foliations -- 4.4. The commuting sheaf C(M, F) -- 4.5. Transversally complete foliations -- 4.6. The Atiyah sequence and developability -- 4.7. Exercises -- 5 The Structure of Riemannian Foliations -- 5.1. The lifted foliation -- 5.2. The structure of the leaf closures -- 5.3. The commuting sheaf and the second structure theorem -- 5.4. The orbits of the global transverse fields -- 5.5. Killing foliations -- 5.6. Riemannian foliations of codimension 1, 2 or 3 -- 5.7. Exercises -- 6 Singular Riemannian Foliations -- 6.1. The notion of a singular Riemannian foliation -- 6.2. Stratification by the dimension of the leaves -- 6.3. The local decomposition theorem -- 6.4. The linearized foliation -- 6.5. The global geometry of SRFs -- 6.6. Exercises -- Appendix A Variations on Riemannian Flows -- Appendix B Basic Cohomology and Tautness of Riemannian Foliations -- Appendix C The Duality between Riemannian Foliations and Geodesible Foliations -- Appendix D Riemannian Foliations and Pseudogroups of Isometries -- Appendix E Riemannian Foliations: Examples and Problems -- References.

بدون عنوان

0

متن يادداشت

Foliation theory has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential equation is defined by a vector field X ; if this vector field has no singularities, then its trajectories form a par tition of M into curves, i.e. a foliation of codimension n - 1. More generally, a foliation F of codimension q on M corresponds to a partition of M into immersed submanifolds [the leaves] of dimension ,--------,- - . - -- p = n - q. The first global image that comes to mind is 1--------;- - - - - - that of a stack of "plaques". 1---------;- - - - - - Viewed laterally [transver 1--------1- - - -- sally], the leaves of such a 1--------1 - - - - -. stacking are the points of a 1--------1--- ----. quotient manifold W of di L..... -' _ mension q. -----~) W M Actually, this image corresponds to an elementary type of folia tion, that one says is "simple". For an arbitrary foliation, it is only l- u L ally [on a "simpIe" open set U] that the foliation appears as a stack of plaques and admits a local quotient manifold. Globally, a leaf L may - - return and cut a simple open set U in several plaques, sometimes even an infinite number of plaques.

شماره استاندارد بين المللي کتاب و موسيقي

9781468486728

عنوان

Springer eBooks

موضوع مستند نشده

Geometry.

موضوع مستند نشده

Global differential geometry.

موضوع مستند نشده

Mathematics.

مستند نام اشخاص تاييد نشده

Molino, Pierre.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190307161700.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y