Geometry of curves and surfaces, spring 2016

Teacher: Marja Kankaanrinta

Scope: 10 cr

Type: Advanced studies

Teaching:

Topics: We begin by studying the curvature and torsion of curves. After that we will study the geometry of surfaces. We will define the normal curvature of a surface and prove a theorem linking the geometry of a surface to linear algebra. We will study the Gauss and mean curvature of a surface and prove Gauss's Theorema Egregium. We will also prove the Gauss-Bonnet theorem for compact surfaces. Time permitting, we will study other topics, for example minimal surfaces.

Prerequisites: Students should know some multivariable calculus. For example, the course Vektorianalyysi (or Vektorianalyysi I and II) give a suitable background. We will also use some basic linear algebra like eigenvalues and eigenvectors.