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
AI总结：
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。
摘要：
本文构建了经典黎曼曲面的四元数与八元数类比版本。这类流形的构造具有独特性质，通过深入研究Bernhard Riemann主要基于共形性的黎曼曲面研究方法，我们定义了四元数与八元数黎曼流形的切片共形（或称切片等温）参数化。这类新的流形类别包含切片正则四元数与八元数曲线、切片正则函数的图像、4维与8维球面，以及螺旋面型和悬链面型的4维与8维流形。借助合适的黎曼流形，我们还给出了四元数与八元数对数函数及n次根函数的统一定义。
英文摘要：
In this paper we establish quaternionic and octonionic analogs of the classical Riemann surfaces. The construction of these manifolds has nice peculiarities and the scrutiny of Bernhard Riemann approach to Riemann surfaces, mainly based on conformality, leads to the definition of slice conformal or slice isothermal parameterization of quaternionic or octonionic Riemann manifolds. These new classes of manifolds include slice regular quaternionic and octonionic curves, graphs of slice regular functions, the $4$ and $8$ dimensional spheres, the helicoidal and catenoidal $4$ and $8$ dimensional manifolds. Using appropriate Riemann manifolds, we also give a unified definition of the quaternionic and octonionic logarithm and $n$-th root function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
