Remarks on Chern–Einstein Hermitian metrics

  • Daniele AngellaEmail author
  • Simone Calamai
  • Cristiano Spotti


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.


Chern connection Chern–Einstein metrics 

Mathematics Subject Classification

53B35 32Q99 53A30 22E25 



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Daniele Angella
    • 1
    Email author
  • Simone Calamai
    • 1
  • Cristiano Spotti
    • 2
  1. 1.Dipartimento di Matematica e Informatica “Ulisse Dini”Università di FirenzeFirenzeItaly
  2. 2.Department of Mathematics, Centre for Quantum Geometry of Moduli SpacesAarhus UniversitetAarhus CDenmark

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