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DIFFERENTIAL GEOMETRY
| academic year: | 2013/2014 |
| instructor: | Alessandro Silva |
| degree course: | Mathematics - DM 270/04 (triennale), III year |
| type of training activity: | caratterizzante |
| credits: | 6 (48 class hours) |
| scientific sector: | MAT/03 Geometria |
| teaching language: | italiano |
| period: | I sem (30/09/2013 - 17/01/2014) |
Lecture meeting time and location
Presence: highly recommended
Suggested readings:
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Differentiable coverings Sard's Theorem Whitney's embedding theorem Frobenius' theorem Preliminaries of Riemannian Geometry - Lee Smooth Manifolds ed Springer Boothby An Introduction to differentiable manifolds and Riemannian geometry ed Academic Press Warner Foundations of differential geometry and Lie groups, ed Scott Foresman
Type of course: standard
Prerequisites:
Algebra lineare, Geometria Analitica, Calcolo 1 e 2; fortemente raccomandato il corso di Topologia (Geometria 2).
Knowledge and understanding:
knowledge of the basic notions of differential geometry of curves and surfaces (arclength, curvature, Frenet apparatus, I and II fundamental forms, area and integration on surfaces, derivation on surfaces, different notions of curvature); knowledge of the metric structure of surfaces and the variational properties of geodesics and minimal surfaces; knowledge of fundamentals of spherical and hyperbolic geometry, and of different kind of plane representations of the sphere (geographical maps); knowledge of the intrinsic differential calculus on a surface, and how it originated the idea of Riemannian manifold.
Skills and attributes:
ability of drawing a plane curve, solving elementary problems on curves with the Frenet apparatus; computation of angles, length, areas for curves and surfaces; ability of determining the tangent space of a submanifold of R^3, of computing the main invariants and interpreting visually the results; ability of solving elementary problems of spherical geometry.
Personal study: the percentage of personal study required by this course is the 65% of the total.