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Keywords:
almost Kähler manifold; quaternionic analysis; regular function in the sense of Fueter
almost Kähler manifold; quaternionic analysis; regular function in the sense of Fueter
Summary:
Using the fundamental notions of the quaternionic analysis we show that there are no 4-dimensional almost Kähler manifolds which are locally conformally flat with a metric of a special form.
References:
[1] Fueter, R.: Die Funktionentheorie der Differentialgleichungen ${\triangle }u=0$ und ${\triangle }{\triangle }u = 0$ mit vier reellen Variablen. Comment. Math. Helv. 7 (1935), 307–330. MR 1509515
[2] Goldberg, S. I.: Integrability of almost Kähler manifolds. Proc. Amer. Math. Soc. 21 (1969), 96–100. MR 0238238 | Zbl 0174.25002
[3] Królikowski, W.: On Fueter-Hurwitz regular mappings. Diss. Math. 353 (1996). MR 1388662
[4] Kobayashi, S., Nomizu, K.: Foundations of differential geometry. I – II, Interscience, 1963. MR 0152974
[5] Sudbery, A.: Quaternionic analysis. Math. Proc. Cambridge Philos. Soc. 85 (1979), 199–225. MR 0516081 | Zbl 1100.30042
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