Properties of Critical Points of the Dinew-Popovici Energy Functional
Recently, Dinew and Popovici introduced and studied an energy functional F acting on the metrics in the Aeppli cohomology class of a Hermitian-symplectic metric and showed that in dimension 3 its critical points (if any) are Kähler. In this article we further investigate the critical points of this...
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-12-01
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| Series: | Complex Manifolds |
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| Online Access: | https://doi.org/10.1515/coma-2021-0144 |
| _version_ | 1811171890357600256 |
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| author | Soheil Erfan |
| author_facet | Soheil Erfan |
| author_sort | Soheil Erfan |
| collection | DOAJ |
| description | Recently, Dinew and Popovici introduced and studied an energy functional F acting on the metrics in the Aeppli cohomology class of a Hermitian-symplectic metric and showed that in dimension 3 its critical points (if any) are Kähler. In this article we further investigate the critical points of this functional in higher dimensions and under holomorphic deformations. We first prove that being a critical point for F is a closed property under holomorphic deformations. We then show that the existence of a Kähler metric ω in the Aeppli cohomology class is an open property under holomorphic deformations. Furthermore, we consider the case when the (2, 0)-torsion form ρω 2, 0 of ω is ∂-exact and prove that this property is closed under holomorphic deformations. Finally, we give an explicit formula for the differential of F when the (2, 0)-torsion form ρω2, 0 is ∂-exact. |
| first_indexed | 2024-04-10T17:22:51Z |
| format | Article |
| id | doaj.art-8a450c879032419ca3e7446329430c8b |
| institution | Directory Open Access Journal |
| issn | 2300-7443 |
| language | English |
| last_indexed | 2024-04-10T17:22:51Z |
| publishDate | 2022-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Complex Manifolds |
| spelling | doaj.art-8a450c879032419ca3e7446329430c8b2023-02-05T08:30:37ZengDe GruyterComplex Manifolds2300-74432022-12-019135536910.1515/coma-2021-0144Properties of Critical Points of the Dinew-Popovici Energy FunctionalSoheil Erfan0Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062Toulouse, FranceRecently, Dinew and Popovici introduced and studied an energy functional F acting on the metrics in the Aeppli cohomology class of a Hermitian-symplectic metric and showed that in dimension 3 its critical points (if any) are Kähler. In this article we further investigate the critical points of this functional in higher dimensions and under holomorphic deformations. We first prove that being a critical point for F is a closed property under holomorphic deformations. We then show that the existence of a Kähler metric ω in the Aeppli cohomology class is an open property under holomorphic deformations. Furthermore, we consider the case when the (2, 0)-torsion form ρω 2, 0 of ω is ∂-exact and prove that this property is closed under holomorphic deformations. Finally, we give an explicit formula for the differential of F when the (2, 0)-torsion form ρω2, 0 is ∂-exact.https://doi.org/10.1515/coma-2021-0144deformation theoryhermitian-symplectic metricskähler manifolds51m1551m16 |
| spellingShingle | Soheil Erfan Properties of Critical Points of the Dinew-Popovici Energy Functional Complex Manifolds deformation theory hermitian-symplectic metrics kähler manifolds 51m15 51m16 |
| title | Properties of Critical Points of the Dinew-Popovici Energy Functional |
| title_full | Properties of Critical Points of the Dinew-Popovici Energy Functional |
| title_fullStr | Properties of Critical Points of the Dinew-Popovici Energy Functional |
| title_full_unstemmed | Properties of Critical Points of the Dinew-Popovici Energy Functional |
| title_short | Properties of Critical Points of the Dinew-Popovici Energy Functional |
| title_sort | properties of critical points of the dinew popovici energy functional |
| topic | deformation theory hermitian-symplectic metrics kähler manifolds 51m15 51m16 |
| url | https://doi.org/10.1515/coma-2021-0144 |
| work_keys_str_mv | AT soheilerfan propertiesofcriticalpointsofthedinewpopovicienergyfunctional |