5 credits
30.0 h + 30.0 h
Q1
Teacher(s)
Haine Luc;
Language
French
Prerequisites
The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
Content
In 2018-2019, the course will address the basic notions of differential and riemannian geometry.
- Differentiable manifolds, immersions, submersions, embeddings, examples.
- Vector fields, Lie bracket.
- Differential forms, Stokes-Cartan formula.
- Riemannian geometry, curvature, Poincaré-Hopf theorem and its link with the Gauss-Bonnet formula.
One of the goal of the class is to show how topological invariants of varieties manifest themselves through the study of vector fields, differential forms and riemannian metrics.
Differential geometry is the basis for the study of the modern developments in mechanics, in particular in symplectic geometry, as well as in general relativity.
- Differentiable manifolds, immersions, submersions, embeddings, examples.
- Vector fields, Lie bracket.
- Differential forms, Stokes-Cartan formula.
- Riemannian geometry, curvature, Poincaré-Hopf theorem and its link with the Gauss-Bonnet formula.
One of the goal of the class is to show how topological invariants of varieties manifest themselves through the study of vector fields, differential forms and riemannian metrics.
Differential geometry is the basis for the study of the modern developments in mechanics, in particular in symplectic geometry, as well as in general relativity.
Bibliography
Syllabus disponible sur Moodle.
Référence bibliographique:
L. Godinho, J. Natário, An Introduction to Riemannian Geometry, with Applications to Mechanics and Relativity, Springer UTX 2014.
Référence bibliographique:
L. Godinho, J. Natário, An Introduction to Riemannian Geometry, with Applications to Mechanics and Relativity, Springer UTX 2014.
Faculty or entity
MATH
