Differential Geometry: A First Course in Curves and Surfaces

Title	:	Differential Geometry: A First Course in Curves and Surfaces
Authors	:	Theodore Shifrin
	:	Preliminary Version; Fall, 2015

CURVES

1. Examples, Arclength Parametrization
2. Local Theory: Frenet Frame
3. Some Global Results

SURFACES: LOCAL THEORY

1. Parametrized Surfaces and the First Fundamental Form
2. The Gauss Map and the Second Fundamental Form
3. The Codazzi and Gauss Equations and the Fundamental Theorem of Surface Theory
4. Covariant Differentiation, Parallel Translation, and Geodesics

SURFACES: FURTHER TOPICS

1. Holonomy and the Gauss-Bonnet Theorem
2. An Introduction to Hyperbolic Geometry
3. Surface Theory with Differential Forms
4. Calculus of Variations and Surfaces of Constant Mean Curvature

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