Canonical metrics on holomorphic Courant algebroids

The solution of the Calabi Conjecture by Yau implies that every Kähler Calabi–Yau manifold (Formula presented.) admits a metric with holonomy contained in (Formula presented.), and that these metrics are parameterized by the positive cone in (Formula presented.). In this work, we give evidence of an...

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Detalles Bibliográficos
Autores: García Fernández, Mario, Rubio, Roberto, Shahbazi, Carlos, Tipler, Carl
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/716351
Acceso en línea:http://hdl.handle.net/10486/716351
https://dx.doi.org/10.1112/plms.12468
Access Level:acceso abierto
Palabra clave:Calabi Conjecture
Courant algebroids
Complex surfaces
Holomorphic string algebroids
Matemáticas
Descripción
Sumario:The solution of the Calabi Conjecture by Yau implies that every Kähler Calabi–Yau manifold (Formula presented.) admits a metric with holonomy contained in (Formula presented.), and that these metrics are parameterized by the positive cone in (Formula presented.). In this work, we give evidence of an extension of Yau's theorem to non-Kähler manifolds, where (Formula presented.) is replaced by a compact complex manifold with vanishing first Chern class endowed with a holomorphic Courant algebroid (Formula presented.) of Bott–Chern type. The equations that define our notion of best metric correspond to a mild generalization of the Hull–Strominger system, whereas the role of (Formula presented.) is played by an affine space of ‘Aeppli classes’ naturally associated to (Formula presented.) via Bott–Chern secondary characteristic classes