 Aims
The course presents the fundamental notions of differential geometry. It serves as a basis to other course of geometry in the masters' years of mathematical sciences.
Main themes
The course contains three parts:
1: A description of the basic objects of geometry: manifolds, fiber bundles, vector fields, differential forms, Lie bracket, differential of an application, immersion, submersion. Various examples: Lie groups, homogeneous spaces, projective spaces and Grassmannian manifolds.
2: A presentation of the basic elements of Riemann geometry: parallel transport, particular case of surfaces, curves, geodesics, etc.
3: Applications to mechanics and an overview of important theorems of geometry; Arnold-Liouville, tores geometry, Hamilton mechanics, etc.
Other credits in programs
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MAP21
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Première année du programme conduisant au grade d'ingénieur civil en mathématiques appliquées
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(5 credits)
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MATH21/E
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Première licence en sciences mathématiques (Economie mathématique)
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(5 credits)
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Mandatory
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MATH21/G
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Première licence en sciences mathématiques (Général)
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(5 credits)
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Mandatory
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MATH21/S
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Première licence en sciences mathématiques (Statistique)
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(5 credits)
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Mandatory
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