Author | Molino, Pierre. author |
---|---|
Title | Riemannian Foliations [electronic resource] / by Pierre Molino |
Imprint | Boston, MA : Birkhรคuser Boston, 1988 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-8670-4 |
Descript | XII, 344 p. online resource |
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