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 caltech.edu
Office Hours:  
Tuesdays, 11 am



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Announcements
 

 


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
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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.



Policies
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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.


Textbooks
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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
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Date Description
   

Handouts
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Date Description
   

Homework
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Due Date Homework  Solutions
October 16

HW1

 
November 6 - NEW! (October 30 - old)
HW2
 
November 14
HW3
 
December 2
HW4
 
December 12
HW5
 


 
     


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