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Rigidity results for Riemannian twistor spaces under vanishing curvature conditions.
- Source :
- Annals of Global Analysis & Geometry; Mar2023, Vol. 63 Issue 2, p1-44, 44p
- Publication Year :
- 2023
-
Abstract
- 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 C P 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0232704X
- Volume :
- 63
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Annals of Global Analysis & Geometry
- Publication Type :
- Academic Journal
- Accession number :
- 162069800
- Full Text :
- https://doi.org/10.1007/s10455-023-09889-x