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Rigidity results for Riemannian twistor spaces under vanishing curvature conditions
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Journal Article
Rigidity results for Riemannian twistor spaces under vanishing curvature conditions
2023
Overview
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 CP3 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.
Publisher
Springer Nature B.V
Subject
