Twistor Spaces of Riemannian Manifolds with Even Clifford Structures

TL;DR

This paper introduces the concept of twistor spaces for Riemannian manifolds with even Clifford structures, generalizing existing notions and exploring their complex and metric properties.

Contribution

It defines twistor spaces for even Clifford structures and investigates their complex structures and metric geometries, extending previous frameworks.

Findings

Constructed almost complex structures on twistor spaces.

Proved integrability of these structures in certain cases.

Established conditions for Kähler and Nearly-Kähler metrics.

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-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.