Twistor spaces of Riemannian manifolds with even Clifford structures

Abstract

In this paper, we introduce the twistor space of a Riemannian manifold with an even Clifford structure. This notion generalizes the twistor space of quaternion-Hermitian manifolds and weak- $$\mathrm {Spin}(9)$$ structures. We also construct almost complex structures on the twistor space for parallel even Clifford structures and check their integrability. Moreover, we prove that in some cases one can give Kahler and nearly Kahler metrics to these spaces.