DIFFERENTIAL GEOMETRY

Credit Hours: 3 · Undergraduate Upper-Level

MATH 402 is the undergraduate version of the graduate class MATH 500 (being generic for all related instances of dual enrollment classes). This is a 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 500 . Mutually Exclusive: Cannot register for MATH 402 if student has credit for MATH 500 .