2007 Fall MATH 268-01
Bulletin Course Description Lie groups and related topics, Hodge theory, index theory, minimal surfaces, Yang-Mills fields, exterior differential systems, harmonic maps, symplectic geometry. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title DIFFERENTIAL GEOMETRY Department MATH Course Number 2007 Fall 268 Section Number 01 Primary Instructor Lee,Dan A Permission required? N
Prerequisites
Math 267, or equivalent knowledge of differentiable manifolds and the basics of Riemannian geometry (metric, connection, curvature, geodesics). Some knowledge of differential equations is also useful.
Synopsis of course content
Most of this course will be a standard course in Riemannian geometry, picking up where Math 267 leaves off. Topics may include isometric immersions, Gauss-Bonnet, Jacobi fields and Morse theory, Bonnet-Myers, Cartan-Hadamard, Cartan-Ambrose-Hicks, Rauch, Bishop-Gromov, Toponogov, Soul Theorem, Splitting Theorem, Hodge Theorem, and the Bochner technique.
Textbooks
TBA, but it will be something like do Carmo or Petersen.
Assignments
sporadic homework assignments, some of which should be turned in
Exams
no exams
Term Papers
no papers
Grade to be based on
homework, participation
Additional Information
Students might be assigned to present certain topics. Please email dalee@math.duke.edu if you have any questions.
Help with searching
