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Remarks on Chern–Einstein Hermitian metrics

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We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.

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Acknowledgements

The authors are grateful to Stefan Ivanov, Fabio Podestà, Valentino Tosatti, Yury Ustinovskiy for several useful discussions on the subject. During the preparation of this note, the first two named authors have been supported by the Project PRIN “Varietà reali e complesse: geometria, topologia e analisi armonica”, by the Project SIR2014 “Analytic aspects in complex and hypercomplex geometry” (AnHyC) code RBSI14DYEB, and by GNSAGA of INdAM. DA is further supported by project FIRB “Geometria Differenziale e Teoria Geometrica delle Funzioni” ’, and SC by the Simons Center for Geometry and Physics, Stony Brook University. The third-named author is supported by AUFF Starting Grant 24285, Villum Young Investigator 0019098, and DNRF95 QGM “Centre for Quantum Geometry of Moduli Spaces”.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica “Ulisse Dini”, Università di Firenze, viale Morgagni 67/a, 50134, Firenze, Italy

    Daniele Angella & Simone Calamai

  2. Department of Mathematics, Centre for Quantum Geometry of Moduli Spaces, Aarhus Universitet, Building 1530, Office 330 Ny Munkegade 118, Aarhus C, 8000, Denmark

    Cristiano Spotti

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  1. Daniele Angella
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  2. Simone Calamai
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  3. Cristiano Spotti
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Correspondence to Daniele Angella.

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Angella, D., Calamai, S. & Spotti, C. Remarks on Chern–Einstein Hermitian metrics. Math. Z. 295, 1707–1722 (2020). https://doi.org/10.1007/s00209-019-02424-4

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