1. Canonical metrics on holomorphic Courant algebroids
- Author
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Mario Garcia‐Fernandez, Roberto Rubio, Carlos Shahbazi, Carl Tipler, Instituto de Ciencias Matematicas (ICMAT), Universidad Autónoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de Bretagne Atlantique (LMBA), Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS), ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), Laboratoire de mathématiques de Brest ( LM ), Université de Brest ( UBO ) -Institut Brestois du Numérique et des Mathématiques ( IBNM ), Université de Brest ( UBO ) -Centre National de la Recherche Scientifique ( CNRS ), HEP, INSPIRE, Laboratoire de mathématiques de Brest (LM), Université de Brest (UBO)-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS), and Universidad Autonoma de Madrid (UAM)-Consejo Superior de Investigaciones Científicas [Madrid] (CSIC)
- Subjects
Mathematics - Differential Geometry ,High Energy Physics - Theory ,geometry ,[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th] ,space: Calabi-Yau ,General Mathematics ,[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] ,FOS: Physical sciences ,[PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph] ,holomorphic ,[ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th] ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,Differential Geometry (math.DG) ,High Energy Physics - Theory (hep-th) ,Mathematics - Symplectic Geometry ,[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] ,FOS: Mathematics ,Symplectic Geometry (math.SG) ,[PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th] ,[ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph] ,holonomy ,Mathematics::Differential Geometry ,Algebraic Geometry (math.AG) ,Mathematics::Symplectic Geometry - Abstract
The solution of the Calabi Conjecture by Yau implies that every K\"ahler Calabi-Yau manifold $X$ admits a metric with holonomy contained in $\textrm{SU}(n)$, and that these metrics are parametrized by the positive cone in $H^{1,1}(X,\mathbb{R})$. In this work we give evidence of an extension of Yau's theorem to non-K\"ahler manifolds, where $X$ is replaced by a compact complex manifold with vanishing first Chern class endowed with a holomorphic Courant algebroid $Q$ 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 $H^{1,1}(X,\mathbb{R})$ is played by an affine space of 'Aeppli classes' naturally associated to $Q$ via Bott-Chern secondary characteristic classes., Comment: 55 pages, Lemma 2.2 fixed, presentation improved, appendix added, to appear in the Proceedings of the London Mathematical Society
- Published
- 2022