Course Schedule and Catalog
Course Catalog - 2024-2025
MATH 500 - DIFFERENTIAL GEOMETRY
Long Title: DIFFERENTIAL GEOMETRY
Department: Mathematics
Grade Mode: Standard Letter
Language of Instruction: Taught in English
Course Type: Lecture
Credit Hours: 3
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
Prerequisite(s): MATH 444 OR MATH 539
Description: A graduate course in smooth and Riemannian manifolds. Tensors, Riemannian metrics, differential forms. Lie derivatives. Distributions and foliations, including the Frobenius Theorem and an introduction to contact structures. Lie groups and the exponential map. Connections on Vector Bundles. Geodesics and completeness. Curvature. First and second variations of length and area. Jacobi Fields. Additional topics may vary from year to year. Graduate/Undergraduate Equivalency: MATH 402. Mutually Exclusive: Cannot register for MATH 500 if student has credit for MATH 402. Repeatable for Credit.