This class will be a continuation of Differential Geometry I (Math 6455). We will study various notions of curvature both for surfaces in Euclidean 3-space as well as abstract manifolds. Topics covered include isometric embeddings and some of the fundamental results in global Riemannian geometry.
Differential Geometry I (Math 6455).
Instructor's notes in addition to excerpts and reference to
An Introduction to Differential Manifolds by Barden and Thomas; Notes on Differetial Geometry by Hicks; and Riemannian Geometry by Do Carmo.
The grade is based largely on class participation (the students are expected to attend all lectures). There may be one or two take home tests as well.