On Bismut--Ambrose--Singer manifolds
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915977177858048 |
|---|---|
| author | Barbaro, Giuseppe Pediconi, Francesco |
| author_facet | Barbaro, Giuseppe Pediconi, Francesco |
| contents | We investigate Bismut--Ambrose--Singer (BAS) manifolds, namely Hermitian manifolds whose Bismut connection has parallel torsion and parallel curvature. We first establish a canonical reduction theorem for complete, simply-connected BAS manifolds. We then classify simply-connected BAS manifolds in the three fundamental homogeneous settings: the compact case, the non-compact semisimple case, and the nilpotent case. Building on this, we construct BAS manifolds in which these three geometries are combined, generalizing all previously known examples. Finally we classify complete, simply-connected, pluriclosed BAS manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02485 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Bismut--Ambrose--Singer manifolds Barbaro, Giuseppe Pediconi, Francesco Differential Geometry Complex Variables We investigate Bismut--Ambrose--Singer (BAS) manifolds, namely Hermitian manifolds whose Bismut connection has parallel torsion and parallel curvature. We first establish a canonical reduction theorem for complete, simply-connected BAS manifolds. We then classify simply-connected BAS manifolds in the three fundamental homogeneous settings: the compact case, the non-compact semisimple case, and the nilpotent case. Building on this, we construct BAS manifolds in which these three geometries are combined, generalizing all previously known examples. Finally we classify complete, simply-connected, pluriclosed BAS manifolds. |
| title | On Bismut--Ambrose--Singer manifolds |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2605.02485 |