Textbook: M. DoCarmo "Riemannian
geometry." This is one of the best (if not the best) introductory books on
Riemannian geometry. I will also occasionally use handouts which will
be posted on the class' homepage.
This course is a continuation of
240A.
In this course we will cover chapters 5, 7-10 of DoCarmo's "Riemannian
geometry". The key issue addressed in 240-B is: What is the geometric meaning of the
Riemannian curvature? Cartan-Hadamard theorem and Rauch
comparison theorem are the highlights of 240-B.
I will assign weekly homework which will be used to grade the course. I
will assign the homework on Mondays (or Wednesdays in the case of a
holiday) and collect it a week later.
The lectures will start on January 4. January 18 and February 15 are
holidays. The last day of classes is March 15. There will be no classes
during the week March 8-12 since I will be out of town (in Banff,
Canada) organizing a conference.