The 4-Planes of Spin(7) Manifolds
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916263374094336 |
|---|---|
| author | Yalcinkaya, Eyup |
| author_facet | Yalcinkaya, Eyup |
| contents | This paper investigates the geometric structures and properties of 8-dimensional manifolds with Spin(7)-holonomy. We focus on the characterization and implications of 4-planes within these manifolds, which are endowed with an almost symplectic structure compatible with the Spin(7)-structure. We provide a detailed analysis of the differential forms defining these structures, including the Cayley 4-form and its stabilization under the Spin(7) group actions. Furthermore, we explore the concept of mirror duality within the context of exceptional holonomy, elucidating the relationship between dual structures and their topological constraints. By examining the conditions under which mirror duality arises, we enhance the understanding of the interplay between Spin(7)-structures and symplectic geometry. This endeavor contributes to our deeper understanding of the intricate symmetries and topological properties of these remarkable manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17936 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The 4-Planes of Spin(7) Manifolds Yalcinkaya, Eyup Differential Geometry 53C38, 53D05, 53D15, 57R17 This paper investigates the geometric structures and properties of 8-dimensional manifolds with Spin(7)-holonomy. We focus on the characterization and implications of 4-planes within these manifolds, which are endowed with an almost symplectic structure compatible with the Spin(7)-structure. We provide a detailed analysis of the differential forms defining these structures, including the Cayley 4-form and its stabilization under the Spin(7) group actions. Furthermore, we explore the concept of mirror duality within the context of exceptional holonomy, elucidating the relationship between dual structures and their topological constraints. By examining the conditions under which mirror duality arises, we enhance the understanding of the interplay between Spin(7)-structures and symplectic geometry. This endeavor contributes to our deeper understanding of the intricate symmetries and topological properties of these remarkable manifolds. |
| title | The 4-Planes of Spin(7) Manifolds |
| topic | Differential Geometry 53C38, 53D05, 53D15, 57R17 |
| url | https://arxiv.org/abs/2405.17936 |