Riemannian Geometry

The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.

Résumé

"Perhaps it could best be described as an excellent monograph on geodesics which has been expanded to include an introduction to the preliminary ideas which this requires. [...] The main subject of this book is exciting and new results are constantly being obtained. Any differential geometer should know something about geodesics and this is a good place to read about it, as well as to find many useful ideas and examples for reference." Mathematical Reviews (review of the first edition)

"Now in its second edition, this textbook continuous to offer the probably best introduction to the topics in Riemannian geometry which are centred around the theory of geodesics." Zentralblatt für Mathematik