Quasi-conformal functions of quaternion and octonion variables, their integral transformations

四元数与八元数上的切片共形性与黎曼流形

Slice conformality and Riemann manifolds on quaternions and octonions

该研究借鉴黎曼共形性思路，定义四元数与八元数黎曼流形的切片共形参数化，涵盖多类典型流形，并给出四元数、八元数对数与n次根函数的统一定义。

Structure of wrap groups of quaternion and octonion fiber bundles

This article is devoted to the investigation of structure of wrap groups of connected fiber bundles over the fields of real $\bf R$, complex $\bf C$ numbers, the quaternion skew field $\bf H$ and the octonion algebra $\bf O$. Iterated wrap groups are studied as well. Their smashed products are constructed.

Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables

This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of functions are defined and investigated. Four criteria of a family being normal are proven. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated. It is proven, that they are finite dimensional Lie groups for compact manifolds. Their examples are given. Many charactersitic features are found in comparison with commutative geometry over $\bf R$ or $\bf C$.

Zeros of regular functions of quaternionic and octonionic variable: a division lemma and the camshaft effect

We study in detail the zero set of a regular function of a quaternionic or octonionic variable. By means of a division lemma for convergent power series, we find the exact relation existing between the zeros of two octonionic regular functions and those of their product. In the case of octonionic polynomials, we get a strong form of the fundamental theorem of algebra. We prove that the sum of the multiplicities of zeros equals the degree of the polynomial and obtain a factorization in linear polynomials.

Affine and wrap algebras over octonions

The article is devoted to affine and wrap algebras over quaternions and octonions. Residues of functions of quaternion and octonion variables are studied. They are used for construction of such algebras. Their structure is investigated.

Convergence of Taylor Series of real normed division algebras

We propose a new way to compute the radius of convergence for Quaternionic hyperholomorphic functions and for Octonion analytic functions. We extend the theorem of Cauchy Hadamard and the theorem of Abel on convergence of series to Quaternionic analysis with the Fueter Operator, to Quaternionic analysis with the Moisil Theodoresco operator and to the Octonion analysis with the Fueter operator.