Differential Geometry III

Michaelmas 2019 - Epiphany 2020

Time and place:   Lectures: Tuesday 14:00, CM101
Thursday 11:00, CM101
Problems classes:   Friday 10:00, CM101, Weeks 4,6,8,10
Instructor: Anna Felikson
e-mail: anna dot felikson at durham dot ac dot uk
Office: CM124; Phone: 334-4158
Office hours: Tuesday 11:30 - 12:30 and by appointment

Textbooks: The lectures are based on the following books. Although we will not follow any of these strictly, the material can be found in them.

Preliminary course content (subject to change): Plane and space curves, arc length, tangent and normal vectors, curvature, local and global properties; embedded surfaces, tangent planes, curves on surfaces; intrinsic geometry of a surface, metric, length, area, first fundamental form; maps between surfaces, Gauss map; isometries and conformal maps, the Weingarten map, the second fundamental form, Gauss curvature and mean curvature, minimal surfaces, Theorema Egregium, Christoffel symbols, normal and geodesic curvatures, Meusnier's theorem, asymptotic curves, lines of curvature, geodesics, Clairaut's relations, global and local Gauss--Bonnet theorems.

Schedule (preliminary):

If you have any questions you are very welcome to ask (during the lectures, after a lecture, during office hours, in any other convenient time or via e-mail)!!!


  • There will be weekly sets of exercises; stared questions to hand in on Thursdays, weeks 3,5,7,9. and weeks 13,15,17,19. -- (+/- notation used for marking)
  • Course materials:

    Some applications of differential geometry:

    Fun: ----

    More Animations: ----

    Who is who: ---- Riemann, ---- Serret, ---- Frenet, ---- Jacobi, ---- Gauss, ---- Christoffel, ---- Weingarten, ---- Caratheodory, ---- Meusnier, ---- Clairaut, ---- Bonnet. ----