A Panoramic View of Riemannian Geometry

Berger M.

In his latest book A Panoramic View of Riemannian Geometry, Marcel Berger does a remarkable job giving an in-depth survey ranging over almost the full spectrum of Riemannian geometry, furnishing the reader with some of the most exciting and elegant topics from classical to modern, and from local to global Riemannian geometry.The reader will find that, unlike many other books on Riemannian geometry, the style of this 15-chapter 824-page manuscript is quite unique. The author does not follow the traditional definition-theorem-proof approach; instead, he only motivates and presents, without detailed proofs, the best possible results in many areas known to date, thereby providing interested readers with a valuable source and efficient means for learning about the latest advances. Additionally, throughout the book, open problems are introduced and discussed as soon as they can be stated. The organization of the material in this book also distinguishes itself from many of its peers – as Berger says, “in our division into chapters, necessarily arbitrary, we did not follow any logical or historical order. We have tried to follow certain naturalness and simplicity.”