Chern flat manifolds that are torsion-critical
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915232920633344 |
|---|---|
| author | Zhang, Dongmei Zheng, Fangyang |
| author_facet | Zhang, Dongmei Zheng, Fangyang |
| contents | In our previous work, we introduced a special type of Hermitian metrics called {\em torsion-critical,} which are non-Kähler critical points of the $L^2$-norm of Chern torsion over the space of all Hermitian metrics with unit volume on a compact complex manifold. In this short note, we restrict our attention to the class of compact Chern flat manifolds, which are compact quotients of complex Lie groups equipped with compatible left-invariant metrics. Our main result states that, if a Chern flat metric is torsion-critical, then the complex Lie group must be semi-simple, and conversely, any semi-simple complex Lie group admits a compatible left-invariant metric that is torsion-critical. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chern flat manifolds that are torsion-critical Zhang, Dongmei Zheng, Fangyang Differential Geometry 53C55 In our previous work, we introduced a special type of Hermitian metrics called {\em torsion-critical,} which are non-Kähler critical points of the $L^2$-norm of Chern torsion over the space of all Hermitian metrics with unit volume on a compact complex manifold. In this short note, we restrict our attention to the class of compact Chern flat manifolds, which are compact quotients of complex Lie groups equipped with compatible left-invariant metrics. Our main result states that, if a Chern flat metric is torsion-critical, then the complex Lie group must be semi-simple, and conversely, any semi-simple complex Lie group admits a compatible left-invariant metric that is torsion-critical. |
| title | Chern flat manifolds that are torsion-critical |
| topic | Differential Geometry 53C55 |
| url | https://arxiv.org/abs/2411.01132 |