Twistor spaces of Riemannian manifolds with even Clifford structures

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• 作者：Gerardo Arizmendi ; Charles Hadfield
• 关键词：Clifford structure ; Twistor spaces ; Almost complex structure ; Nearly Kähler ; Kähler ; Grassmannian
• 刊名：Annals of Global Analysis and Geometry
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：51
• 期：1
• 页码：11-20
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Statistics for Business/Economics/Mathematical Finance/Insurance; Theoretical, Mathematical and Computational Physics; Group Theory and Generalizations; Geometry;
• 出版者：Springer Netherlands
• ISSN：1572-9060
• 卷排序：51

文摘

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 Kähler and nearly Kähler metrics to these spaces.