Non-Kähler Calabi-Yau geometry and pluriclosed flow
Hermitian, pluriclosed metrics with vanishing Bismut-Ricci form give a natural extension of Calabi-Yau metrics to the setting of complex, non-Kähler manifolds, and arise independently in mathematical physics. We reinterpret this condition in terms of the Hermitian-Einstein equation on an associated...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/708775 |
| Acceso en línea: | http://hdl.handle.net/10486/708775 https://dx.doi.org/10.1016/j.matpur.2023.07.002 |
| Access Level: | acceso abierto |
| Palabra clave: | Bismut connection Calabi-Yau Pluriclosed flow Matemáticas |
| Sumario: | Hermitian, pluriclosed metrics with vanishing Bismut-Ricci form give a natural extension of Calabi-Yau metrics to the setting of complex, non-Kähler manifolds, and arise independently in mathematical physics. We reinterpret this condition in terms of the Hermitian-Einstein equation on an associated holomorphic Courant algebroid, and thus refer to solutions as Bismut Hermitian-Einstein. This implies MumfordTakemoto slope stability obstructions, and using these we exhibit infinitely many topologically distinct complex manifolds in every dimension with vanishing first Chern class which do not admit Bismut Hermitian-Einstein metrics. This reformulation also leads to a new description of pluriclosed flow in terms of Hermitian metrics on holomorphic Courant algebroids, implying new global existence results, in particular on all complex non-Kähler surfaces of Kodaira dimension κ ≥ 0. On complex manifolds which admit Bismut-flat metrics we show global existence and convergence of pluriclosed flow to a Bismut-flat metric, which in turn gives a classification of generalized Kähler structures on these spaces |
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