This course will be an introduction to Riemannian geometry.

Instructor: Professor C. Robin Graham

Meeting Time: MWF 1:30--2:20

Location: C-401 Padelford

Office Hours: MW 2:30-3:30 in C-549 Padelford, or other times by appt.

TEXTBOOK:

The textbook for this course is "Introduction to Riemannian Manifolds, Second Edition", by our own Jack Lee. This new edition is not quite yet published; it will probably be commercially available within the next month or two. Jack has kindly agreed to make a near final draft version available to students registered in our course.

There is a condition associated to your use of this draft version of the book:

Jack is making the book available for your temporary personal use as a student in this course. It is copyrighted material. By viewing or downloading the book, you agree not to share, reproduce, or disseminate it in any form without express written permission.

Please respect Jack's generosity in letting us have early access to the book by honoring these terms.

I urge you not to print out this draft version of the book. The published version will be coming out soon, and it will be a little different, mostly corrections of typos. You should plan to acquire a copy of the final version when it becomes available.

Registered students in the course can temporarily access the book here.

Jack is eager to be notified of typos or suggestions via email at johnmlee@uw.edu. Probably it is too late for any typos you find to be corrected in the published version, but Jack maintains a web page of corrections for each of his books and he will post any typos you find there. And, who knows, maybe there will be a third edition someday where your suggestions make it into print!

READING AND HOMEWORK:

There will be no exams.

A reading and homework assignment will be posted here approximately every other week. The reading is the essential part of the course. You are strongly encouraged to do all the Exercises as you read. They are interspersed as an integral part of the text. The lectures will usually follow the textbook fairly closely but will sometimes refer to the text for details.

Homework assignments will be graded and returned. Your course grade will be based on the homework. You are encouraged to work together on the homework, but please write up your own solutions in your own words.

RESERVE BOOKS:

You are assumed to be familiar with the material covered in the Manifolds course Math 544/545/546, which is contained in the two books:

• [ITM] J. Lee, Introduction to Topological Manifolds, 2nd edition, Springer, 2011.
• [ISM] J. Lee, Introduction to Smooth Manifolds, 2nd edition, Springer, 2013.

These two books will be on reserve in the Math Research Library. They are also available online to UW students via the Math Research Library website.

The following books will also be on reserve in the Math Research Library. You may want to consult them for further information and for other treatments of Riemannian geometry.

• M. do Carmo, Riemannian Geometry, Birkhauser, 1992.
• P. Petersen, Riemannian Geometry, 2nd edition, Springer, 2006. (also available online via the Math Research Library website.)
• M. Spivak, A Comprehensive Introduction to Differential Geometry Vols. I--V, Publish or Perish, 1979.
• J. Cheeger and D. G. Ebin, Comparison Theorems in Riemannian Geometry, AMS, 2008.

Mathematics Department

University of Washington