Rigidity results for Riemannian twistor spaces under vanishing curvature conditions
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909310932484096 |
|---|---|
| author | Catino, Giovanni Dameno, Davide Mastrolia, Paolo |
| author_facet | Catino, Giovanni Dameno, Davide Mastrolia, Paolo |
| contents | In this paper we provide new rigidity results for four-dimensional Riemannian manifolds and their twistor spaces.In particular, using the moving frame method, we prove that $\mathbb{CP}^3$ is the only twistor space whose Bochner tensor is parallel; moreover, we classify Hermitian Ricci-parallel and locally symmetric twistor spaces and we show the nonexistence of conformally flat twistor spaces. We also generalize a result due to Atiyah, Hitchin and Singer concerning the self-duality of a Riemannian four-manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_14865 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Rigidity results for Riemannian twistor spaces under vanishing curvature conditions Catino, Giovanni Dameno, Davide Mastrolia, Paolo Differential Geometry In this paper we provide new rigidity results for four-dimensional Riemannian manifolds and their twistor spaces.In particular, using the moving frame method, we prove that $\mathbb{CP}^3$ is the only twistor space whose Bochner tensor is parallel; moreover, we classify Hermitian Ricci-parallel and locally symmetric twistor spaces and we show the nonexistence of conformally flat twistor spaces. We also generalize a result due to Atiyah, Hitchin and Singer concerning the self-duality of a Riemannian four-manifold. |
| title | Rigidity results for Riemannian twistor spaces under vanishing curvature conditions |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2206.14865 |