Riemannian Geometry: Edition 3

Important revisions to the third edition include:

• a substantial addition of unique and enriching exercises scattered throughout the text;
  
• inclusion of an increased number of coordinate calculations of connection and curvature;
  
• addition of general formulas for curvature on Lie Groups and submersions;
  
• integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger;
  
• incorporation of several recent results about manifolds with positive curvature;
  
• presentation of a new simplifying approach to the Bochner technique for tensors with application to bound topological quantities with general lower curvature bounds.
  

From reviews of the first edition:

"The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type."

―Bernd Wegner, ZbMATH