English

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The aim of the course is to give the graduate student good knowledge about important concepts for the mathematical description of smooth two dimensional surfaces in space.

Geometry for hypersurfaces in Euclidean spaces. The Gauss map, curvature, focal points, minimal surfaces, convex surfaces, the Gauss-Bonnet theorem in two dimensions.

be able to account for basic concepts of differential geometry such as principal curvatures, Gaussian curvature, mean curvature and, geodesics.
be able to explain how the principal curvatures in a point determine the local shape of the surface near the point.
be able to explain how knowledge about how the Gaussian curvature varies over the surface gives information about the global form of the surface.

Föreläsningar

Seminarier

Skriftlig tentamen

Muntlig tentamen

Inlämningsuppgifter

Compulsory assignments may occur.

Underkänd, godkänd

At least 60 hp mathematics.

Calculus in several variables including vector analysis in three dimensions.

Gudmundsson, S.: An Introduction to Gaussian Geometry. Centre for Mathematical Sciences, Lund University, 2017.

MATM13F

 -08-24

Professor Thomas Johansson