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 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
Kähler-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.
Readership
Graduate students and researchers interested in
the generalized Ricci Flow and mathematical physics.
