On 4-dimensional locally conformally flat almost Kaehler manifolds

W. Krolikowski

Motylowa 4/27, 91-360 Lodz, Poland

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

AMSclassification. 15A63, 15A66, 30G35, 30G99, 32A30, 53C10 - 53C40, 53C55.


Keywords. Almost K{\"a}hler manifold, quaternionic analysis, regular function in the sense of Fueter.