Department of Physics

10ΕΛΕ12 Geometry II

Course webpage:  https://eclass.uoa.gr/courses/MATH640

Course outline

Course content

• Regular curves. Arc length. Parametrization with respect to arc length. Curvature and torsion. Frenet­-Serret frame. Fundamental theorem of curves.
• Regular surfaces. Tangent plane.
• Gauss map and shape operator.
• Second fundamental form. Principal curvatures. Gauss curvature and mean curvature. Isometries.
• Gauss Theorema Egregium. Intrinsic geometry. Geodesics.
• Gauss-Bonnet theorem.