Math 157a
Riemannian Geometry
Fall 2014-15
TR 9:00 AM // 106 ANB
Course Description | Policies | Textbooks | Lecture Notes | Handouts | Homework | Sections

Instructor:  Maria Trnkova, 280 Sloan, 626-395-4369, mtrnkova at
Office Hours:  
Tuesdays, 11 am

Feedback Form


09/26/14 If you find the course schedules inconvenient we can work on it and shift to 10:30 am.
10/29/14 The due date of the HW2 was postponed for one week.
10/30/14 I will add topics for the oral presentation here.

Course Description

The goal of the course is to define basic concepts of Riemannian Geometry (metric, connection, geodesics, curvature, completeness, exponential map), to study the relationships between geodesics and curvature (Jacobi field) and connection between local and global properties of Riemannian Manifolds (e.g. Hopf-Rinow, Hadamard Theorems). We also consider spaces of constant curvature.


Grading: Grading is based on home works.

Homework Policy: There will be five home works (every second week). One home work can be replaced by an oral presentation for ~20 minutes of a topic in Riemannian Geometry. Collaborations are allowed but write your own solution.
Homeworks should be handed in at the beginning of a class at 9 am in 106 ANB. The due date will be written on the list of problems.


1) Gallot, Hulin and Lafontaine, Riemannian Geometry, Springer-Verlag, Universitext, 3rd edition or later. ISBN-13: 978-3540204930, ISBN-10: 3540204938, 2004.

2) Do Carmo, Riemannian Geometry, Birkhäuser Boston, ISBN-13: 978-0817634902, ISBN-10: 0817634908, 1992.

3) Lee, Riemannian Manifolds: An Introduction to Curvature, Springer, ISBN 978-0-387-98271-7, 1997.

Lecture Notes

Date Description


Date Description


Due Date Homework  Solutions
October 16


November 6 - NEW! (October 30 - old)
November 14
December 2
December 12


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