Generalized Ricci flow
Author(s)
Bibliographic Information
Generalized Ricci flow
（University lecture series, v. 76）
American Mathematical Society, c2021
- : pbk
Available at 17 libraries
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbkGAR||41||1200041773470
Note
Includes bibliographical references (p. 241-248)
Description and Table of Contents
Description
The generalized Ricci flow is a geometric evolution equation which has recently emerged from investigations into mathematical physics, Hitchin's generalized geometry program, and complex geometry. This book gives an introduction to this new area, discusses recent developments, and formulates open questions and conjectures for future study. The text begins with an introduction to fundamental aspects of generalized Riemannian, complex, and Kahler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields natural extensions of Einstein and Calabi-Yau structures as `canonical metrics' in generalized Riemannian and complex geometry. The book then introduces generalized Ricci flow as a tool for constructing such metrics and proves extensions of the fundamental Hamilton/Perelman regularity theory of Ricci flow. These results are refined in the setting of generalized complex geometry, where the generalized Ricci flow is shown to preserve various integrability conditions, taking the form of pluriclosed flow and generalized Kahler-Ricci flow, leading to global convergence results and applications to complex geometry. Finally, the book gives a purely mathematical introduction to the physical idea of T-duality and discusses its relationship to generalized Ricci flow. The book is suitable for graduate students and researchers with a background in Riemannian and complex geometry who are interested in the theory of geometric evolution equations.
Table of Contents
Introduction
Generalized Riemannian Geometry
Generalized Connections and Curvature
Fundamentals of Generalized Ricci Flow
Local Existence and Regularity
Energy and Entropy Functionals
Generalized Complex Geometry
Canonical Metrics in Generalized Complex Geometry
Generalized Ricci Flow in Complex Geometry
T-duality
Bibliography.
by "Nielsen BookData"