Chern-Ricci flow and t-Gauduchon Ricci-flat condition
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916687694004224 |
|---|---|
| author | Correa, Eder M. Galindo, Giovane Grama, Lino |
| author_facet | Correa, Eder M. Galindo, Giovane Grama, Lino |
| contents | In this paper, we study the $t$-Gauduchon Ricci-flat condition under the Chern-Ricci flow. In this setting, we provide examples of Chern-Ricci flow on compact non-Kähler Calabi-Yau manifolds which do not preserve the $t$-Gauduchon Ricci-flat condition for $t<1$. The approach presented generalizes some previous constructions on Hopf manifolds. Also, we provide non-trivial new examples of balanced non-pluriclosed solution to the pluriclosed flow on non-Kähler manifolds. Further, we describe the limiting behavior, in the Gromov-Hausdorff sense, of geometric flows of Hermitian metrics (including the Chern-Ricci flow and the pluriclosed flow) on certain principal torus bundles over flag manifolds. In this last setting, we describe explicitly the Gromov-Hausdorff limit of the pluriclosed flow on principal $T^{2}$-bundles over the Fano threefold ${\mathbb{P}}(T_{{\mathbb{P}^{2}}})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chern-Ricci flow and t-Gauduchon Ricci-flat condition Correa, Eder M. Galindo, Giovane Grama, Lino Differential Geometry Complex Variables 53E30, 53C55 (Primary), 32M10, 14M17, 32Q25 (Secondary) In this paper, we study the $t$-Gauduchon Ricci-flat condition under the Chern-Ricci flow. In this setting, we provide examples of Chern-Ricci flow on compact non-Kähler Calabi-Yau manifolds which do not preserve the $t$-Gauduchon Ricci-flat condition for $t<1$. The approach presented generalizes some previous constructions on Hopf manifolds. Also, we provide non-trivial new examples of balanced non-pluriclosed solution to the pluriclosed flow on non-Kähler manifolds. Further, we describe the limiting behavior, in the Gromov-Hausdorff sense, of geometric flows of Hermitian metrics (including the Chern-Ricci flow and the pluriclosed flow) on certain principal torus bundles over flag manifolds. In this last setting, we describe explicitly the Gromov-Hausdorff limit of the pluriclosed flow on principal $T^{2}$-bundles over the Fano threefold ${\mathbb{P}}(T_{{\mathbb{P}^{2}}})$. |
| title | Chern-Ricci flow and t-Gauduchon Ricci-flat condition |
| topic | Differential Geometry Complex Variables 53E30, 53C55 (Primary), 32M10, 14M17, 32Q25 (Secondary) |
| url | https://arxiv.org/abs/2504.09329 |