Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
MAT 240B: Differential Geometry
Approved: 2008-09-01, Michael Kapovich
Units/Lecture:
Winter, every year; 4 units; lecture/term paper or discussion
Suggested Textbook: (actual textbook varies by instructor; check your
instructor)
Prerequisites:
Course 240A; intended primarily for 2nd-year graduate students.
Course Description:
Jacobi fields, conjugate points, completeness, Hopf-Rinow theorem, Cartan-Hadamard theorem, energy, variation theorems and their applications, Rauch comparison theorem and its applications.
Suggested Schedule:
Department Syllabus
| Lectures | Sections | Topics/Comments |
|---|---|---|
| Chapters 5, 7, 9, 10 of do Carmo's book | Jacobi fields, conjugate points, completeness, Hopf-Rinow theorem, Cartan-Hadamard theorem, energy, variation theorems and their applications, Rauch comparison theorem. | |
| Supplementary topics: Index theorem (Chapter 11) or manifolds of negative curvature (Chapter 12) |
Additional Notes:
Supplementary Reading: P. Petersen, Riemannian Geometry