Flat manifolds with holonomy group $\mathbb{Z}_{2}^{k}$ of diagonal type
Flat manifolds with holonomy group $\mathbb{Z}_{2}^{k}$ of diagonal type
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对角型完整群 $mathbb{Z}_{2}^{k}$ 的平坦流形
DOI：
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发表时间：
2014
期刊：
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通讯作者：
A. Szczepański
中科院分区：
文献类型：
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作者：
A. Gąsior;A. Szczepański
我们考虑了两类具有对角型完整群Z2的平坦流形之间的关系：实Bott流形的RBM族和广义Hantzsche-Wendt流形的GHW族。特别地，我们证明了交GHW∩径向基M不是空的。此外，我们还考虑了一类不具有自旋和自旋C结构的实Bott流形。这种结构的存在是有条件的(定理1)。作为应用，给出了所有无自旋结构的5维实Bott流形的列表。
We consider relations between two families of flat manifolds with holonomy group Z2 of diagonal type: the family RBM of real Bott manifolds and the family GHW of generalized Hantzsche-Wendt manifolds. In particular, we prove that the intersection GHW∩RBM is not empty. Moreover, we consider some class of real Bott manifolds without Spin and SpinC structure. There are given conditions (Theorem 1) for the existence of such structures. As an application a list of all 5-dimensional oriented real Bott manifolds without Spin structure is given.