Differential Geometry in Physics (Lecture Notes)
Differential Geometry and Physics
Lectures Notes by Gabriel Lugo, University of North Carolina at Wilmington
Book Content
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 R3
4.1 Manifolds
4.2 First Fundamental form
4.3 Second Fundamental Form
4.4 Curvature
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