## 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