SUBJECT
Title
Topics in differential geometry
Type of instruction
lecture
Level
master
Faculty
Part of degree program
Credits
2
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
Differential geometric characterization of convex surfaces. Steiner-Minkowski formula, Herglotz integral formula, rigidity theorems for convex surfaces.
Ruled surfaces and line congruences.
Surfaces of constant curvature. Tchebycheff lattices, Sine-Gordon equation, Bäcklund transformation, Hilbert’s theorem. Comparison theorems.
Variational problems in differential geometry. Euler-Lagrange equation, brachistochron problem, geodesics, Jacobi fields, Lagrangian mechanics, symmetries and invariants, minimal surfaces, conformal parameterization, harmonic mappings.
Readings
- W. Blaschke: EinfĂĽhrung in die Differentialgeometrie. Springer-Verlag, 1950.
- J. A. Thorpe: Elementary Topics in Differential Geometry. Springer-Verlag, 1979.
- J. J. Stoker: Differential Geometry. John Wiley & Sons Canada, Ltd.; 1989.
- F. W. Warner: Foundations of Differentiable Manifolds and Lie Groups. Springer-Verlag, 1983.