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Softcover ISBN:  9781470462581 
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Softcover ISBN:  9781470462581 
Product Code:  ULECT/76 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
eBook ISBN:  9781470464110 
Product Code:  ULECT/76.E 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
Softcover ISBN:  9781470462581 
eBook ISBN:  9781470464110 
Product Code:  ULECT/76.B 
List Price:  $110.00 $82.50 
MAA Member Price:  $99.00 $74.25 
AMS Member Price:  $88.00 $66.00 

Book DetailsUniversity Lecture SeriesVolume: 76; 2021; 248 ppMSC: Primary 53
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 Kähler geometry. This leads to an extension of the classical EinsteinHilbert action, which yields natural extensions of Einstein and CalabiYau 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 KählerRicci flow, leading to global convergence results and applications to complex geometry. Finally, the book gives a purely mathematical introduction to the physical idea of Tduality 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.
ReadershipGraduate students and researchers interested in the generalized Ricci Flow and mathematical physics.

Table of Contents

Chapters

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

Tduality


Additional Material

Reviews

Generalized geometry is still a young field, and even expository accounts are generally found in papers. In the authors' words, "The primary purpose of this book is to provide an introduction to the fundamental geometric, algebraic, topological, and analytic aspects of the generalized Ricci flow equation." Many results about generalized geometry and generalized Ricci flow are currently open. The authors note, "The secondary purpose of this book is to formulate questions and conjectures about the generalized Ricci flow as an invitation to the reader."
Andrew D. Hwang, College of the Holy Cross


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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 Kähler geometry. This leads to an extension of the classical EinsteinHilbert action, which yields natural extensions of Einstein and CalabiYau 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 KählerRicci flow, leading to global convergence results and applications to complex geometry. Finally, the book gives a purely mathematical introduction to the physical idea of Tduality 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.
Graduate students and researchers interested in the generalized Ricci Flow and mathematical physics.

Chapters

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

Tduality

Generalized geometry is still a young field, and even expository accounts are generally found in papers. In the authors' words, "The primary purpose of this book is to provide an introduction to the fundamental geometric, algebraic, topological, and analytic aspects of the generalized Ricci flow equation." Many results about generalized geometry and generalized Ricci flow are currently open. The authors note, "The secondary purpose of this book is to formulate questions and conjectures about the generalized Ricci flow as an invitation to the reader."
Andrew D. Hwang, College of the Holy Cross