Twistor Spaces of Riemannian Manifolds with Even Clifford Structures

Gerardo Arizmendi; Charles Hadfield

Twistor Spaces of Riemannian Manifolds with Even Clifford Structures

Differential Geometry 2016-02-15 v1

Authors: Gerardo Arizmendi , Charles Hadfield

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.

Keywords

twistor space Riemannian manifold even Clifford structure quaternion-Hermitian manifold weak Spin(9) structure almost complex structure Kähler metric

Cite

@article{arxiv.1602.04159,
  title  = {Twistor Spaces of Riemannian Manifolds with Even Clifford Structures},
  author = {Gerardo Arizmendi and Charles Hadfield},
  journal= {arXiv preprint arXiv:1602.04159},
  year   = {2016}
}

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11 pages, 4 tables

Twistor Spaces of Riemannian Manifolds with Even Clifford Structures

Abstract

Keywords

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