Differential Geometry and Homogeneous Spaces

1 Manifolds.- 2 Vector Bundles and Tensors.- 3 Riemannian Manifolds.- 4 The Poincare-Hopf Theorem and the Chern-Gauss-Bonnet Theorem.- 5 Geodesics.- 6 Homogeneous Spaces.- 7 Symmetric Spaces.- 8 General Relativity.- A Solutions to Selected Exercises.

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• Física Matemática
• Geometria diferencial e riemaniana
• Grupos e teoria do grupo

Differential geometry;Differential topology;Manifolds;Riemannian geometry;curvature;Homogeneous space;Symmetric space;Vector bundle;Global Analysis;Lorentz group;Lie group;Relativity;Connection;Levi-Civita;de Rham cohomology;fibre bundle;Lie algebra;parallel transport;Ricci curvature;geodesic