Spin(9) geometry of the octonionic Hopf fibration
Spin(9) geometry of the octonionic Hopf fibration
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八元 Hopf 纤维的 Spin(9) 几何
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
V. Vuletescu
中科院分区：
文献类型：
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作者：
L. Ornea;M. Parton;P. Piccinni;V. Vuletescu
我们根据对称群Spin(9)给出的结构，讨论了八元离子霍普夫纤维S15→S8的黎曼性质。特别地，我们证明了任何垂直向量场至少有一个零，从而证明了S1子颤的不存在性。然后从共形的角度讨论了自旋(9)-结构，并确定了紧致局部共形平行自旋(9)-流形的结构。最后，我们给出了一系列局部共形平行自旋(9)-流形的例子。
We deal with Riemannian properties of the octonionic Hopf fibration S15 → S8, in terms of the structure given by its symmetry group Spin(9). In particular, we show that any vertical vector field has at least one zero, thus reproving the non-existence of S1 subfibrations. We then discuss Spin(9)-structures from a conformal viewpoint and determine the structure of compact locally conformally parallel Spin(9)-manifolds. Eventually, we give a list of examples of locally conformally parallel Spin(9)-manifolds.