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Ricci flow on Courant algebroids

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arxiv 2402.11069 v1 pith:JP36HIDL submitted 2024-02-16 math.DG math-phmath.APmath.MP

Jeffrey Streets , Charles Strickland-Constable , Fridrich Valach This is my paper · ORCID
classification math.DGmath-phmath.APmath.MP
keywords flowriccicourantsolutionsalgebroidsgeneralizedprovetheory
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We develop a theory of Ricci flow for metrics on Courant algebroids which unifies and extends the analytic theory of various geometric flows, yielding a general tool for constructing solutions to supergravity equations. We prove short time existence and uniqueness of solutions on compact manifolds, in turn showing that the Courant isometry group is preserved by the flow. We show a scalar curvature monotonicity formula and prove that generalized Ricci flow is a gradient flow, extending fundamental works of Hamilton and Perelman. Using these we show a convergence result for certain nonsingular solutions to generalized Ricci flow.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Exterior Generalised Geometry

    math.DG 2025-07 conditional novelty 7.0 of 10

    This paper develops a submanifold calculus for exact Courant algebroids: generalised second fundamental form, Gauss-Codazzi equations, constraint equations, and a fundamental theorem for hypersurfaces.

  2. Courant Algebroid Relations, T-Dualities and Generalised Ricci Flow

    hep-th 2025-02 conditional novelty 6.0 of 10

    Using Courant algebroid relations, the authors prove that geometric T-duality maps solutions of generalized Ricci flow to solutions of generalized Ricci flow, preserving the generalized string background equations.

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