Riemannian geometry books to read after Lee's "Riemannian Manifolds: An Introduction to Curvature"

Question

I have recently completed the book Riemannian Manifolds: An Introduction to Curvature by Lee. I want more advanced text book or monographs on Riemannian geometry with this background. Any suggestion would be much appreciated.

Answer 1

Petersen's Riemannian Geometry includes the topics in Lee's book, but also many more.

You might also be interested in Besse's Einstein Manifolds which is more advanced.

Answer 2

If you are learning by yourself, I think the best option is to find books which have many exercises and solutions to them. Since you already studied John Lee's book, an excellent text to continue your journey on Riemannian Geometry would be Sakai's book with the same title (it includes problems with solutions). Another good book is Chavel's one, which has a section on "Hints and Sketches for Exercises". With these two books you can be sure that you will have a solid background in Riemannian Geometry.