18.950 - Differential Geometry (Spring 2018)

Schedule

Note: The schedule is subject to change. Check back for changes and updates

TOPICS BY LECTURE (with do Carmo references)

Wed, Feb 7: 1.1-1.5, 2.3 Regular parametrized curves, Frenet Frames. (Notes)
Mon Feb 12: 1.5, 1.6 Local Canonical Form. Fundamental Theorem of Curve Theory.(Notes)
Wed Feb 14: 1.7 Isoperimetric Inequality, Global Theory. (Notes)
Tue Feb 20: 2.2, 2.3 Introduction to Surfaces, Differentials. (Notes)
Wed Feb 21: 2.3, 2.4 Differentials, Tangent Spaces. (Notes)
Mon Feb 26: 2.5 The First Fundamental Form. (Notes)
Wed Feb 28: 2.5, 2.6 Area, Orientation. (Notes)
Mon Mar 5: 2.6 Orientation (Notes)
Wed Mar 7: 3.1-3.2 Gauss Map, Second Fundamental Form (Notes)
Mon Mar 12: 3.3 Local Coordinates (Notes)
Wed Mar 14: 3.4, 3.5 Vector Fields, Minimal Surfaces (Notes)
Mon Mar 19: 4.2 Isometries, Conformal Maps (Notes)
Wed Mar 21: Midterm Midterm
Mon Apr 2: 4.2, 4.3 Christoffel Symbols (Notes)
Wed Apr 4: 4.3 Christoffel Symbols, Theorema Egregium (Notes)
Mon Apr 9: 4.3, 5.2 Fundamental Theorem of Surface Theory, Compact surfaces of constant Gaussian curvature (Notes)
Wed Apr 11: 5.2, 4.4 Parallel Transport (Notes)
Wed Apr 18: 4.4 Geodesics (Notes)
Mon Apr 23: 4.4 Geodesic Curvature (Notes)
Wed Apr 25: 4.5 Clairaut's Relation, Gauss-Bonnet (Notes)
Mon Apr 30: 4.5, 4.6 Gauss-Bonnet, Exponential Map (Notes)
Wed May 2: 4.6, 5.3 Minding's Theorem, Complete Surfaces (Notes)
Mon May 7: 5.3, 5.10 Hopf-Rinow, Abstract Surfaces (Notes)
Wed May 9: 5.10 The Hyperbolic Plane (Notes)
Mon May 14: Shifrin, Section 3.3 Differential Forms in Differential Geometry (Notes)