八元数是四元数的非结合推广与Yang-Mills 方程、黑洞、弦论和狭义相对论密切相关。本项目研究多八元数的分析理论，它是多复变函数论向非交换、非结合领域的推广。近年来，随着多八元数分析理论的不断完善，公开的问题是用复几何的方法研究非齐次Cauchy-Riemann方程、超曲面上Poincare-Bertrand公式。本项目针对上述问题，利用构造复形、Clifford分析中处理非交换的技巧以及八元数特有的结合子研究多八元数分析。它的成功实施将丰富八元数理论的研究内容和方法，为其在物理中的应用提供新鲜血液。

Octonion is a generalization of quaternion to nonassociative algebra which has closed relation with Yang-Mills equations, black hole, string theory and special relativity. Octonion analysis of several variables is a generalization of several complex variables to noncommutative and nonassociative field. Recently, analysis of octonion of several variables is in progressive development. An open problem arises to establish the solvability of the non-homogeneous Cauchy-Riemann equations with using complex geometry as well as Poincare-Bertrand formula in hypersurface. The purpose of this project is to solve the problem by constructing Cauchy-Riemann complex and applying analytic techniques from theory of several complex variables together with the technique dealing with non-commutativity in Clifford analysis. The new approach will enrich octonion analysis of several variables so that it will give new energy for the development of physics.