Manifolds and differential geometry
Jeffrey M. Lee
- Providence, R.I. : American Mathematical Society, c2009
- xiv, 671 p. ill. 27 cm
- Graduate studies in mathematics ; vol. 107 .
- Graduate studies in mathematics ; .
Bibliografie p. 663 Index p. 667
Differentiable manifolds -- The tangent structure -- Immersion and submersion -- Curves and hypersurfaces in Euclidean space -- Lie groups -- Fiber bundles -- Tensors -- Differential forms -- Integration and Stokes' theorem -- De Rham cohomology -- Distributions and Frobenius' theorem -- Connections and covariant derivatives -- Riemannian and semi-Riemannian geometry -- Appendix A: The language of category theory -- Appendix B: Topology -- Appendix C: Some calculus theorems -- Appendix D: Modules and multilinearity.