New Geometric Interpretation of Quaternionic Fueter Functions

Introduction It is interesting that using the properties of quaternionic regular functions in the sense of Fueter, one can obtain the significant results in complex analysis (see, e.g. [1], [3]). There are many amazing relations between quaternionic functions and some objects of complex analysis. This paper is devoted to show one of them, namely that there is a correspondence between quaternionic regular functions in the sense of Fueter and fundamental 2-forms on a 4-dimensional almost Kahler manifold.