Riv. Mat. Univ. Parma, Vol. 13, No. 2, 2022
Nicoletta Tardini ^{[a]}
Hodge theory on almostHermitian manifolds
Pages: 419437
Received: 30 November 2021
Accepted: 5 May 2022
Mathematics Subject Classification: 53C15; 58A14; 58J05.
Keywords: Almostcomplex; 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
''FILQuota Incentivante'' of University of Parma and cosponsored by Fondazione Cariparma
Full Text (PDF)
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 almostHermitian 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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