Data di Pubblicazione:
2023
Citazione:
Rigidity results for Riemannian twistor spaces under vanishing curvature conditions / G. Catino, D. Dameno, P. Mastrolia. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - 63:2(2023), pp. 13.1-13.44. [10.1007/s10455-023-09889-x]
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 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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Twistor space; Four-manifold; Bochner tensor; Weyl tensor; Local conformal flatness; Moving frames;
Elenco autori:
G. Catino, D. Dameno, P. Mastrolia
Link alla scheda completa: