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.
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|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)|