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)
M. do Carmo, Riemannian Geometry ($55)
Search by ISBN on Amazon: 0817634908

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