MAT 484 2.0 Differential Geometry and Manifolds

Course:  MAT 484 2.0 Differential Geometry and Manifolds (Optional)

Course Content:

Regular curves; Local theory of curves parameterized by arc length; Global properties of plane curves; Isoperimetric inequality, four-vertex theorem; Regular surfaces; Tangent plane; Geometry of Gauss map; Ruled surfaces and minimal surfaces; The intrinsic geometry of surfaces; Gauss-Bonnet theorem and its applications; Introduction to manifolds; Riemannian manifolds, Tangent space, Riemannian metrics, Riemannian connection

Recommended Readings:

1. 1. Kuhnel W., Differential Geometry: Curves – Surfaces – Manifolds, third edition, American Mathematical Society, Vol. 77, 2015.
   2. Do Carmo M.P., Differential geometry of curves and surfaces, revised and updated second edition, Dover Publications, 2017.
   3. Shfrin T., DIFFERENTIAL GEOMETRY: A First Course in Curves and Surfaces Preliminary Version Summer, 2016