Differential Geometry in Physics  

Lectures Notes by Gabriel Lugo


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 1Forms 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 R^{3
}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 R^{3
}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 

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 NPFormalism 8.4 SU(3) 
IX. Fiber Bundles 9.1, Fiber Bundles 9.2 Principal Bundles 9.3 Connections on PFB 9.4 Gauge Fields 
09/20/2021
The full book is published by UNC Press and is also available in Amazon. ISBN 9781469669243 (cloth: alk. paper)

Lecture Notes (pdf 3.5 Mb) 
The Lecture Notes here is a short version which only includes the chapters covered in our onesemester course in differential geometry. In the list above, this would be chapters 14 and chapter 6. Thank you all for supporting higher learning 
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Gabriel G. Lugo, lugo@uncw.edu
Last updated
August 05, 2022