University of California at San DiegoDifferential Geometry- by J. FillmoreMath150A- Winter 2001 - is divided into fourteen "lectures" with exercises.LectureCourse information, references, outline, historical 0 Introduction - The theorems of Gauss-Bonnet and Poincaré-Hopf 1 Curves in space - Local theory 2 Curves in space - Some global theorems Ref: R.A. Horn, On Fenchel's theorem, Amer. Math. Monthly 78 1971 380-381, MR0284918 3 Surfaces in space - First fundamental form 4a Surfaces in space - Second fundamental form 4b Example - Surfaces of revolution 5 Surfaces in space - The Gauss map 6a Surfaces in space - Geodesics 6b Surfaces in space - Intrinsic derivatives 6c Example - Surfaces of revolution 7 Abstract surfaces - Local notions 8 Abstract surfaces - Global notions 9 Abstract surfaces - Parallel transport 10 Abstract surfaces - Theorem of Gauss and Bonnet Additional problems Additional problems from Spring 1971 course Problem set for "final exam"Additions to Lecturesas numbered 6 Surfaces in space - Compatibility conditions: Weingarten and Codazzi-Mainardi 6 Surfaces in space - Special parameter curves 6 Surfaces in space - Liebmann's Theorem 7 Abstract surfaces - Shortest arcs, Whitehead's Theorem 7 Abstract surfaces - Geodesic polar coördinates, the exponential map 9 Abstract surfaces - details of calculation of Lecture 9, p.6 ff.Two additional lecturesfrom an earlier course 13a Abstract surfaces - Vector fields on surfaces 13b Abstract surfaces - Theorem of Poincaré and Hopf 14a Non-euclidean - Non-euclidean geometries 14b Non-euclidean - Models of the Lobachevsky plane 14c Non-euclidean - The Poincaré model 14d Non-euclidean - TrigonometryAdditional references150APotpourriCalculating curvature and torsion with arbitrary parameterizations Weingarten's equations Principal directions and Rodrigues's formula Normal curvature and Meusner's theorem Gauss curvature in orthogonal and geodesic polar coördinates Jacobi's equation Geodesics on a sphere from the differential equations - fragments - see Lecture 6c Problem 6.12 Exercise on conformal transformations and stereographic projection