Cover
Title page
Chapter 1. Introduction
1.1. Outline
1.2. On pedagogy
1.3. Acknowledgments
Chapter 2. Generalized Riemannian Geometry
2.1. Courant algebroids
2.2. Symmetries of the Dorfman bracket
2.3. Generalized metrics
2.4. Divergence operators
Chapter 3. Generalized Connections and Curvature
3.1. Generalized connections
3.2. Metric compatible connections
3.3. The classical Bismut connection
3.4. Curvature and the first Bianchi identity
3.5. Generalized Ricci curvature
3.6. Generalized scalar curvature
3.7. Generalized Einstein-Hilbert functional
Chapter 4. Fundamentals of Generalized Ricci Flow
4.1. The equation and its motivation
4.2. Examples
4.3. Maximum principles
4.4. Invariance group and solitons
4.5. Low dimensional structure
Chapter 5. Local Existence and Regularity
5.1. Variational formulas
5.2. Short time existence
5.3. Curvature evolution equations
5.4. Smoothing estimates
5.5. Results on maximal existence time
5.6. Compactness results for generalized metrics
Chapter 6. Energy and Entropy Functionals
6.1. Generalized Ricci flow as a gradient flow
6.2. Expander entropy and Harnack estimate
6.3. Shrinking Entropy and local collapsing
6.4. Corollaries on nonsingular solutions
Chapter 7. Generalized Complex Geometry
7.1. Linear generalized complex structures
7.2. Generalized complex structures on manifolds
7.3. Courant algebroids and pluriclosed metrics
7.4. Generalized KΓ€hler geometry
Chapter 8. Canonical Metrics in Generalized Complex Geometry
8.1. Connections, torsion, and curvature
8.2. Canonical metrics in complex geometry
8.3. Examples and rigidity results
Chapter 9. Generalized Ricci Flow in Complex Geometry
9.1. KΓ€hler-Ricci flow
9.2. Pluriclosed flow
9.3. Generalized KΓ€hler-Ricci flow
9.4. Reduced flows
9.5. Torsion potential evolution equations
9.6. Higher regularity from uniform parabolicity
9.7. Metric evolution equations
9.8. Sharp existence and convergence results
Chapter 10. T-duality
10.1. Topological T-duality
10.2. T-duality and Courant algebroids
10.3. Geometric T-duality
10.4. Buscher rules and the dilaton shift
10.5. Einstein-Hilbert action
10.6. Examples
Bibliography
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