Canonical metrics on holomorphic Courant algebroids

Mario Garcia-Fernandez*, Roberto Rubio*, Carlos Shahbazi, Carl Tipler

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

14 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)700-758
Number of pages59
JournalProceedings of the London Mathematical Society
Issue number3
Publication statusPublished - Sept 2022


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