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arXiv · 2206.14865

Rigidity results for Riemannian twistor spaces under vanishing curvature conditions

Giovanni Catino·Davide Dameno·Paolo Mastrolia
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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 $\mathbb{CP}^3$ 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.

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Giovanni Catino, Davide Dameno, Paolo Mastrolia. 2022-06-29. Rigidity results for Riemannian twistor spaces under vanishing curvature conditions. https://arxiv.org/abs/2206.14865

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