正交乘法是保持模长的双线性映射。 正交乘法与调和映照， 等参超曲面等领域有紧密联系。本文主要讨论[3,4,p]型正交乘法的分类。 为了讨论这个问题， 我们结合Parker和Toth关于正交乘法的分类方法， 对[3,4,8]型正交乘法的模空间给出了显式的代数参数。 我们的分类结果表明[3,4,8]型正交乘法的模空间由两部分组成， 一个5维的模空间和一个3维的退化模空间。 随后我们运用这个方法证明了[3,4,7]型正交乘法的模空间为1维并给出了其代数参数。 与所有关于初等模空间的研究一样， 我们讨论了其边界点的等同而得到实际的模空间。

Orthogonal multiplications are norm-preserving bilinear maps. Orthogonal multiplications have been connected with harmonic maps, isoparametric hypersurfaces and many other areas. The main theme of this thesis is an algebraic classification of such orthogonal multiplications of type [3,4,8]. To this end, we combine Parker's algebraic approach and Toth's moduli space approach. Our classification shows that the moduli space of orthogonal multiplications of type [3,4,8] consist of two components, a 5-dimensional moduli and a 3-dimensional degenerate moduli. In addition, we show that the moduli space of orthogonal multiplications of type [3,4,7] is 1-dimensional. As is the case for any coarse fundamental domain, we discussed the boundary identification to "glue" the domain into the actual moduli space.