An introduction to the differential geometry of curves and surfaces.
Topics in Modern Geometry, a coursepak by Saul Stahl.
MATH 660 or permission of instructor.
- Surfaces in R : Tangent planes, Gaussian curvature, the First Fundamental Form, Sectional curvatures, Geodesics, Gauss's theorem for geodesic polygons, polyhedral surfaces, intrinsic geometry.
- Rudiments of Riemannian geometry: Riemann metrics, geodesics, isometries, curvature.
- Non-Euclidean geometry: The geometry of the upper-halfplane, neutral geometry, the half-plane theorem of Pythagoras, isometries of the half-plane.
- Topics in spherical geometry and the geometry of complex numbers.
(Stahl 2010 )