On 4-dimensional locally conformally flat almost Kähler manifolds

Wiesław Królikowski

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 3, page 215-223
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Królikowski, Wiesław. "On 4-dimensional locally conformally flat almost Kähler manifolds." Archivum Mathematicum 042.3 (2006): 215-223. <http://eudml.org/doc/249788>.

@article{Królikowski2006,
abstract = {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.},
author = {Królikowski, Wiesław},
journal = {Archivum Mathematicum},
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},
language = {eng},
number = {3},
pages = {215-223},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On 4-dimensional locally conformally flat almost Kähler manifolds},
url = {http://eudml.org/doc/249788},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Królikowski, Wiesław
TI - On 4-dimensional locally conformally flat almost Kähler manifolds
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 3
SP - 215
EP - 223
AB - 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.
LA - eng
KW - almost Kähler manifold; quaternionic analysis; regular function in the sense of Fueter; almost Kähler manifold; quaternionic analysis; regular function in the sense of Fueter
UR - http://eudml.org/doc/249788
ER -

References

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  1. Die Funktionentheorie der Differentialgleichungen ▵ u = 0 und ▵ ▵ u = 0 mit vier reellen Variablen, Comment. Math. Helv. 7 (1935), 307–330. MR1509515
  2. Integrability of almost Kähler manifolds, Proc. Amer. Math. Soc. 21 (1969), 96–100. Zbl0174.25002MR0238238
  3. On Fueter-Hurwitz regular mappings, Diss. Math. 353 (1996). MR1388662
  4. Foundations of differential geometry, I – II, Interscience, 1963. MR0152974
  5. Quaternionic analysis, Math. Proc. Cambridge Philos. Soc. 85 (1979), 199–225. Zbl1100.30042MR0516081

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