Lectures Notes by Gabriel Lugo
University of North Carolina at Wilmington
Copyright 1995,  2004, 2010

Differential Geometry and Physics

I. Vectors and Curves
1.1 Tangent Vectors
1.2 Curves
1.3 Fundamental Theorem of Curves
II. Differential forms
2.1 1-Forms
2.2 Tensors and Forms of Higher Rank
2.3 Exterior Derivatives
2.4 The Hodge-* Operator
III. Connections
3.1 Frames
3.2 Curvilinear Coordinates
3.3 Covariant Derivative
3.4 Cartan Equations
IV Surfaces in R
4.1 Manifolds
4.2 First Fundamental form
4.3 Second Fundamental Form
4.4 Curvature
Full set (DVI 228K) (ver1.8) Full set (PDF 340Kb) (ver1.8)

 


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Gabriel G. Lugo, lugo@uncw.edu
Last updated May 21, 2011