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Hermitian ranks of compact complex manifolds

Authors: Daniele Angella and Adriano Tomassini
Journal: Proc. Amer. Math. Soc. 146 (2018), 2195-2205
MSC (2010): Primary 32Q99, 32C35
Published electronically: February 1, 2018
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Abstract: We investigate degenerate special-Hermitian metrics on compact complex manifolds; in particular, degenerate Kähler and locally conformally Kähler metrics on special classes of non-Kähler manifolds.

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Additional Information

Daniele Angella
Affiliation: Dipartimento di Matematica e Informatica “Ulisse Dini” Università degli Studi di Firenze viale Morgagni 67/a 50134 Firenze, Italy

Adriano Tomassini
Affiliation: Dipartimento di Scienze Matematiche, Fisiche e Informatiche Unità di Matematica e Informatica Università di Parma Parco Area delle Scienze 53/A 43124 Parma, Italy

Keywords: Complex manifold, non-K\"ahler geometry, Hermitian metric, degenerate metric, K\"ahler rank, pluri-closed rank
Received by editor(s): February 2, 2017
Received by editor(s) in revised form: June 28, 2017, June 30, 2017, and August 14, 2017
Published electronically: February 1, 2018
Additional Notes: The first author was supported by the Project PRIN “Varietà reali e complesse: geometria, topologia e analisi armonica”, by the Project FIRB “Geometria Differenziale e Teoria Geometrica delle Funzioni”, by SIR2014 project RBSI14DYEB “Analytic aspects in complex and hypercomplex geometry”, and by GNSAGA of INdAM. The second author was supported by Project PRIN “Varietà reali e complesse: geometria, topologia e analisi armonica” and by GNSAGA of INdAM
Communicated by: Filippo Bracci
Article copyright: © Copyright 2018 American Mathematical Society

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