Geometry of curves and surfaces, spring 2016


Teacher: Marja Kankaanrinta 

Scope: 10 cr

Type: Advanced studies


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.


  •  On Tuesday April 19 there will be no class, since that Tuesday is the department's recreation day.

Teaching schedule

Weeks 3-9 and 11-18, Tuesday 10-12 in room B120 and Thursday 10-12 in room C122. In addition, two hours of exercise classes per week.

Easter Holiday 24.-30.3. 


One can pass the class by attending lectures and doing homework exercises. Alternatively, one can pass the class by taking an exam.


Course material





    Suitable books are, for example,

  1. A.N. Pressley: Elementary Differential Geometry.
  2. John Oprea: Differential Geometry and Its Applications.



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Exercise classes

1.Wednesday 10-12 B321 (period III) / C321 (period IV) Marja Kankaanrinta 

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