ON THE RELATIONSHIPS BETWEEN HOPF FIBRATIONS AND CARTAN HYPERSURFACES IN SPHERES
ON THE RELATIONSHIPS BETWEEN HOPF FIBRATIONS AND CARTAN HYPERSURFACES IN SPHERES
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球体中HOPF纤维与嘉当超曲面的关系
DOI：
10.1142/9789811248108_0009
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
HASHIMOTO Hideya
中科院分区：
文献类型：
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作者：
Sampei Hirose;Jun-ichi Inoguchi;Kenji Kajiwara;Nozomu Matsuura and Yasuhiro Ohta;HASHIMOTO Hideya
赫维茨（Hurwitz）的著名定理指出，赋范（除法）代数与以下四个代数之一同构；实数的域R，复数的域C，四元数的代数H，八元数的非结合代数O。利用这些代数结构，我们可以构造球面上的Hopf超曲面和Cartan超曲面。本文的目的是给出这些Hopf纤维与Cartan超曲面之间的关系。
The famous theorem due to Hurwitz stated that the normed (division) algebra is isomorphic to one of the following four algebras; the field R of real numbers, the field C of complex numbers, the algebra H of quaternions, and the nonassociative algebra O of octonions. By using these algebraic structures, we can construct the Hopf fibrations, and Cartan hypersurfaces in a sphere. The purpose of this paper is to give the relationship between these Hopf fibrations and Cartan hypersurfaces.