Twistor Spaces of Riemannian Manifolds with Even Clifford Structures

Gerardo Arizmendi, Charles Hadfield

Published 2016-02-12Version 1

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-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 K\"ahler and Nearly-K\"ahler metrics to these spaces.