Riv. Mat. Univ. Parma, Vol. 13, No. 2, 2022

Nicoletta Tardini [a]

Hodge theory on almost-Hermitian manifolds

Pages: 419-437
Received: 30 November 2021
Accepted: 5 May 2022
Mathematics Subject Classification: 53C15; 58A14; 58J05.
Keywords: Almost-complex; Hermitian metric; Hodge number.
Author address:
[a]: Università di Parma, Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Parma, Italy

The author is partially supported by GNSAGA of INdAM and has financially been supported by the Programme ''FIL-Quota Incentivante'' of University of Parma and co-sponsored by Fondazione Cariparma

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Abstract: This survey summarizes the results presented in a talk at the conference ''Cohomology of Complex Manifolds and Special Structures, II'' held in Levico Terme in July 2021. An important tool in the study of complex manifolds is provided by cohomology groups and the associated spaces of harmonic forms. However, when the integrability of the complex structure is not assumed it seems that cohomological theory and Hodge theory take two different directions. Here we will deal with the natural spaces of harmonic forms that arise in almost-Hermitian geometry and we will discuss their dependence on the metric. Most of the results are contained in [17] and in [18].

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