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| MATH0464-1 | Differential geometry II
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| Duration : | 30h Th, 10h Pr, 20h Mon. WS |
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| Credits/ECTS : |
| Master in Mathematical Sciences, in-depth approach, 1st year | | Second semester | | 8 |
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| Master in Mathematical Sciences, didactic approach, 1st year | | Second semester | | 8 |
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| Master in Mathematical Sciences, professional focus in management, 1st year | | Second semester | | 8 |
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| Master in Mathematical Sciences, professional focus in computer science, 1st year | | Second semester | | 8 |
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| Master in Mathematical Sciences, specialized approach, 1st year | | Second semester | | 8 |
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| Master in Mathematical Sciences | | Second semester | | 8 |
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| Holder(s) : | Pierre Lecomte |
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| Language : | French language |
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| Course contents : | Differential equations of order two on manifold and linear connections
On studies the geometrical counter part over a smooth manifold of an ordinary differential equation of order two. Special attention is paid to the case of isochronal equation and their exponential map. This very general concept has many useful particular cases: exponential map of Lie groups, exponential map of matrices, of real or complex numbers, affine maps. It leads to the notion of geodesics. Various charactrizations of a second order differential equation are proposed, among which horizontal distributions on the tangent bundle, the case of linear connection corresponding to isochronal equations that can also be described using covariant derivatives. Flat linear connections are also studied. |
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| Prerequisites : | Elements of differential geometry. |
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| Organization : | Details are given at the beginning of the academic year. |
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| Written notes : | A pdf file is avaiable at the http://www.geothalg.ulg.ac.be/GD_Option_I.pdf |
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| Assessment : | Practical organization to be discussed with the student. |
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| Contacts : | http://www.ulg.ac.be/geothalg
plecomte@ulg.ac.be |
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