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Viser: Riemannian Geometry
Riemannian Geometry
Sylvestre Gallot, Dominique Hulin og Jacques Lafontaine
(2004)
Sprog: Engelsk
om ca. 10 hverdage
Detaljer om varen
- 3. Udgave
- Paperback: 322 sider
- Udgiver: Springer Berlin / Heidelberg (Juli 2004)
- Forfattere: Sylvestre Gallot, Dominique Hulin og Jacques Lafontaine
- ISBN: 9783540204930
1.A From submanifolds to abstract manifolds.-
1.B The tangent bundle.-
1.C Vector fields.-
1.D Baby Lie groups.-
1.E Covering maps and fibrations.-
1.F Tensors.-
1.G. Differential forms.-
1.H Partitions of unity.- 2 Riemannian metrics.-
2.A Existence theorems and first examples.-
2.B Covariant derivative.-
2.C Geodesies.-
2.D A glance at pseudo-Riemannian manifolds.- 3 Curvature.-
3.A. The curvature tensor.-
3.B. First and second variation.-
3.C. Jacobi vector fields.-
3.D. Riemannian submersions and curvature.-
3.E. The behavior of length and energy in the neighborhood of a geodesic.-
3.F Manifolds with constant sectional curvature.-
3.G Topology and curvature: two basic results.-
3.H. Curvature and volume.-
3.I. Curvature and growth of the fundamental group.-
3.J. Curvature and topology: some important results.-
3.K. Curvature tensors and representations of the orthogonal group.-
3.L. Hyperbolic geometry.-
3.M. Conformai geometry.- 4 Analysis on manifolds.-4.A. Manifolds with boundary.-
4.B. Bishop inequality.-
4.C. Differential forms and cohomology.-
4.D. Basic spectral geometry.-
4.E. Some examples of spectra.-
4.F The minimax principle.-
4.G Eigenvalues estimates.-
4.H. Paul Levy's isoperimetric inequality.- 5 Riemannian submanifolds.-
5.A. Curvature of submanifolds.-
5.B Curvature and convexity.-
5.C Minimal surfaces.- A Some extra problems.- B Solutions of exercises.- List of figures.