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Differential Geometry in Physics | ||
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Lectures Notes by Gabriel Lugo
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| Links: Syllabus Honor Code |
I. Vectors
and Curves 1.1 Tangent Vectors 1.2 Curves 1.3 Fundamental Theorem of Curves 1.4 Natural Equations |
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 Derivatives 3.4 Cartan's Equations |
| IV. Surfaces in R3 4.1 Manifolds 4.2 First Fundamental form 4.3 Second Fundamental Form 4.4 Curvature 4.5 Fundamental Equations |
V. Geometry of Surfaces in R3 5.1 Surfaces of constant Curvature 5.2 Minimal Surfaces 5.3 Conformal Maps |
VI. Riemannian Geometry 6.1 Riemannian Manifolds 6.2 Submanifolds 6.3 Big D 6.4 Lorentzian Manifolds 6.5 Geodesics 6.6 Gauss Bonnet Theorem |
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| VII. Lie Groups 7.1 Lie Groups 7.2 Lie Algebras |
VIII. Classical Groups in Physics 8.1 Orthogonal Groups 8.2 Lorentz Group 8.3 NP-Formalism 8.4 SU(3) |
IX. Fiber Bundles 9.1, Fiber Bundles 9.2 Principal Bundles 9.3 Connections on PFB 9.4 Gauge Fields |
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