Differential Geometry
- Lectures: Mondays and Thursdays: 15:30-16:55, Room 105
- Moodle: For course announcements and course material.
Course
Outline
- Curves, Arc length, Parametrizations, Local theory of curves, The
isoperimetric inequality.
- Surfaces in Euclidean space, Tangents and derivatives, Normals and
orientability, The first fundamental form.
- Gauss map and the second fundamental form, Geodesics.
- Gaussian, mean and principal curvatures.
- Vector Fields, Rigid Notions and Isometries, Conformal Maps.
- Gauss’ Theorema Egregium.
- The Gauss–Bonnet theorem.
- And depending on time and interest: Minimal Surfaces, Covering Spaces,
The Rigidity of the Sphere, Global geometry of Curves, Riemannian
metrics on surfaces, Covariant Derivatives.
Texts
and References
- M. P. do Carmo, Differential geometry of curves and surfaces. This
will be our main text.
- A. Pressley, Elementary differential geometry, Springer.
- S. Montiel and A. Ros, Curves and surfaces, Graduate Studies in
Mathematics, AMS.
- S. Kobayashi, Differential geometry of curves and surfaces, Springer
Undergraduate Mathematics Series, Springer.
- B. O’Neill, Elementary differential geometry.
Evaluation
Plan
- Final grade: Mid-Semester Exam(40) + Final Exam(60)
- To pass the course (DD), one needs to score at least 35% in the
course. The Final exam will cover the entire course.