Sakai Riemannian Geometry Pdf Book

An Introduction to Riemannian Geometry with Applications to Mechanics and Relativity Leonor Godinho and Jos´e Nat´ario Lisbon, 2004. This volume is an English translation of Sakai's textbook on Riemannian geometry which was originally written in Japanese and published in 1992. The author's intent behind the original book was to provide to advanced undergraduate and graduate students an introduction to modern Riemannian geometry that could also serve as a reference.

• Sakai Riemannian Geometry Pdf Books
• Riemannian Geometry Tutorial

This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci and non-positive sectional curvature.

Sakai Riemannian Geometry Pdf Books

If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research. “This book serves as a comprehensive (yet succinct and accessible) guide to the topology of spaces of Riemannian metrics with a given curvature sign condition. This is one of the most well-studied aspects of moduli spaces of Riemannian metrics but remains a very active area of research, and the reader will find in this book the current state-of-the-art results on the subject.” (Renato G. Bettiol, Mathematical Reviews, October, 2016) “The interplay between analysis, geometry, and topology is clearly laid out in this book; analytic invariants are constructed to elucidate the structure of geometric moduli spaces.

Riemannian Geometry Tutorial

The book is an elegant and concise introduction to the field that puts a number of discrete papers into a coherent focus. A useful bibliography of the subject appears at the end.” (Peter B.

Gilkey, zbMATH 1336.53002, 2016).