| Title:
|
On 4-dimensional locally conformally flat almost Kähler manifolds (English) |
| Author:
|
Królikowski, Wiesław |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
215-223 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
almost Kähler manifold |
| Keyword:
|
quaternionic analysis |
| Keyword:
|
regular function in the sense of Fueter |
| MSC:
|
30G35 |
| MSC:
|
53C15 |
| idZBL:
|
Zbl 1164.53383 |
| idMR:
|
MR2260379 |
| . |
| Date available:
|
2008-06-06T22:48:05Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107999 |
| . |
| Reference:
|
[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 |
| Reference:
|
[2] Goldberg, S. I.: Integrability of almost Kähler manifolds.Proc. Amer. Math. Soc. 21 (1969), 96–100. Zbl 0174.25002, MR 0238238 |
| Reference:
|
[3] Królikowski, W.: On Fueter-Hurwitz regular mappings.Diss. Math. 353 (1996). MR 1388662 |
| Reference:
|
[4] Kobayashi, S., Nomizu, K.: Foundations of differential geometry.I – II, Interscience, 1963. MR 0152974 |
| Reference:
|
[5] Sudbery, A.: Quaternionic analysis.Math. Proc. Cambridge Philos. Soc. 85 (1979), 199–225. Zbl 1100.30042, MR 0516081 |
| . |
