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New geometric interpretation of quaternionic Fueter functions

Królikowski W.

Demonstratio Mathematica

2014

Vol. 47, nr 4

776--783

A correspondence between quaternionic regular functions in the sense of Fueter and fundamental 2-forms on a 4-dimensional almost Kähler manifold is shown.

Quaternionic regular functions in the sense of Fueter and fundamental 2-forms on a 4-dimensional almost Kähler manifold

Królikowski W.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 1

77--83

A correspondence between quaternionic regular functions in the sense of Fueter and fundamental 2-forms on a 4-dimensional almost Kahler manifold is shown.

New property of quaternionic Fueter functions

Królikowski W.

Journal of Applied Mathematics and Computational Mechanics

2013

Vol. 12, nr 2

29--37

We present the result of the theory of quaternionic Fueter regular functions. It is shown that the module of such function ||F(q)||, q := w+ix+jy+kz, cannot be an analytic function in r; r2 := ||q||2 := w2 + x2 + y2 + z2.

Quaternionic condition for the existence of 4-dimensional locally conformally flat almost Kahler manifolds

Królikowski W.

Demonstratio Mathematica

2006

Vol. 39, nr 1

195-202

Using the fundamental notions of the quaternionic analysis we show that there are no 4-dimensional almost Kahler manifolds which are locally conformally flat with a metric of a special form.