# On the Dynamical Behaviour of the Generalized Ricci Flow

@article{Raffero2020OnTD, title={On the Dynamical Behaviour of the Generalized Ricci Flow}, author={Alberto Raffero and Luigi Vezzoni}, journal={arXiv: Differential Geometry}, year={2020} }

Motivated by Muller-Haslhofer results on the dynamical stability and instability of Ricci-flat metrics under the Ricci flow, we obtain dynamical stability and instability results for pairs of Ricci-flat metrics and vanishing 3-forms under the generalized Ricci flow.

## 2 Citations

The Stability of Generalized Ricci Solitons

- Mathematics
- 2022

In [12, 28], it was shown that the generalized Ricci flow is the gradient flow of a functional λ generalizing Perelman’s λ functional for Ricci flow. In this work, we further computed the second…

Ricci-Yang-Mills flow on surfaces and pluriclosed flow on elliptic fibrations

- MathematicsAdvances in Mathematics
- 2022

## References

SHOWING 1-10 OF 32 REFERENCES

Dynamical stability and instability of Ricci-flat metrics

- Mathematics, Physics
- 2013

In this short article, we improve the dynamical stability and instability results for Ricci-flat metrics under Ricci flow proved by Sesum (Duke Math J 133:1–26, 2006) and Haslhofer (Calc Var Partial…

Linear and dynamical stability of Ricci-flat metrics

- Mathematics
- 2004

We can talk about two kinds of stability of the Ricci flow at Ricci flat metrics. One of them is a linear stability, defined with respect to Perelman's functional $\mathcal{F}$. The other one is a…

Perelman’s lambda-functional and the stability of Ricci-flat metrics

- Mathematics
- 2010

In this article, we introduce a new method (based on Perelman’s λ-functional) to study the stability of compact Ricci-flat metrics. Under the assumption that all infinitesimal Ricci-flat deformations…

Generalized Ricci flow on nilpotent Lie groups

- MathematicsForum Mathematicum
- 2021

Abstract We define solitons for the generalized Ricci flow on an exact Courant algebroid. We then define a family of flows for left-invariant Dorfman brackets on an exact Courant algebroid over a…

Pluriclosed Flow and the Geometrization of Complex Surfaces

- MathematicsGeometric Analysis
- 2020

We recall fundamental aspects of the pluriclosed flow equation and survey various existence and convergence results, and the various analytic techniques used to establish them. Building on this, we…

Regularity results for pluriclosed flow

- Mathematics
- 2010

In prior work the authors introduced a parabolic flow of pluriclosed metrics. Here we give improved regularity results for solutions to this equation. Furthermore, we exhibit this equation as the…

A parabolic flow of pluriclosed metrics

- Mathematics
- 2009

We define a parabolic flow of pluriclosed metrics. This flow is of the same family introduced by the authors in \cite{ST}. We study the relationship of the existence of the flow and associated static…

Generalized Ricci Flow

- Mathematics
- 2020

This book gives an introduction to fundamental aspects of generalized Riemannian, complex, and K\"ahler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields…

The entropy formula for the Ricci flow and its geometric applications

- Mathematics
- 2002

We present a monotonic expression for the Ricci flow, valid in all dimensions and without curvature assumptions. It is interpreted as an entropy for a certain canonical ensemble. Several geometric…