Ricci flow on Courant algebroids
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911778823208960 |
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| author | Streets, Jeffrey Strickland-Constable, Charles Valach, Fridrich |
| author_facet | Streets, Jeffrey Strickland-Constable, Charles Valach, Fridrich |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ricci flow on Courant algebroids Streets, Jeffrey Strickland-Constable, Charles Valach, Fridrich Differential Geometry Mathematical Physics Analysis of PDEs 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. |
| title | Ricci flow on Courant algebroids |
| topic | Differential Geometry Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2402.11069 |