Hyosang Kang
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SE420 : Differential Geometry

Differential geometry is a branch of mathematics which has wide applications in Physics, Engineering, Architecture, and Economics. This course introduces important concepts of differential geometry by understandings of curves and surfaces.
  • Curves : regular curves, Frenet formula, isoperimetric inequality, Cauchy-Crofton Formula
  • Surfaces : regular surfaces, differentiable functions, regular values, tangent planes, differentials, area, orientation
  • The first/second fundamental form : isometry, Gauss map, (principal, mean, Gaussian) curvatures,
  • Vector fields : Christofffel symbols, Mainardi-Codazzi equations, covariant derivatives
  • Parallel transport : geodesics, Gauss-Bonnet theorem, length-minimizing curves
  • Exponential map : normal neighborhoods, complete surface
  • Riemannian Geometry : Riemannian manifold, Levi-Civita connection, tangent bundle
  • Tensor : curvature, sectional curvature
  • Basic Lie group theory : left-invariant vector fields, Lie derivatives

Past Syllabus

2017 Fall
2018 Fall
2019 Fall
2020 Fall
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