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Geometric Formalities Along the Chern-Ricci Flow

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In this paper, we study how the notions of geometric formality according to Kotschick and other geometric formalities adapted to the Hermitian setting evolve under the action of the Chern-Ricci flow on class VII surfaces, including Hopf and Inoue surfaces, and on Kodaira surfaces.

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Acknowledgements

This work has been originally developed as partial fulfillment for the second author’s Master Degree in Matematica at Università di Firenze under the supervision of the first author. The authors would like to thank Andrea Cattaneo, José Manuel Moreno-Fernández, Cosimo Flavi, Nicoletta Tardini, and Adriano Tomassini for several interesting discussions. Thanks also to the anonymous Referee for her/his comments and suggestions.

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

    Daniele Angella & Tommaso Sferruzza

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  1. Daniele Angella
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  2. Tommaso Sferruzza
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Correspondence to Daniele Angella.

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Communicated by Filippo Bracci.

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The first author is supported by the Project PRIN “Varietà reali e complesse: geometria, topologia e analisi armonica”, by SIR2014 project RBSI14DYEB “Analytic aspects in complex and hypercomplex geometry”, and by GNSAGA of INdAM.

This article is part of the topical collection “Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, Michael Shapiro and Daniele Struppa.

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Angella, D., Sferruzza, T. Geometric Formalities Along the Chern-Ricci Flow. Complex Anal. Oper. Theory 14, 27 (2020). https://doi.org/10.1007/s11785-019-00971-6

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