Author:
Catino G.,Dameno D.,Mastrolia P.
Abstract
AbstractIn 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 $$\mathbb {C}\mathbb {P}^3$$
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.
Funder
Università degli Studi di Milano
Publisher
Springer Science and Business Media LLC
Subject
Geometry and Topology,Analysis
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