| Title:
|
Almost complex projective structures and their morphisms (English) |
| Author:
|
Hrdina, Jaroslav |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
255-264 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We discuss almost complex projective geometry and the relations to a distinguished class of curves. We present the geometry from the viewpoint of the theory of parabolic geometries and we shall specify the classical generalizations of the concept of the planarity of curves to this case. In particular, we show that the natural class of J-planar curves coincides with the class of all geodesics of the so called Weyl connections and preserving of this class turns out to be the necessary and sufficient condition on diffeomorphisms to become homomorphisms or anti-homomorphisms of almost complex projective geometries. (English) |
| Keyword:
|
linear connection |
| Keyword:
|
geodetics |
| Keyword:
|
$F$-planar |
| Keyword:
|
$A$-planar |
| Keyword:
|
parabolic geometry |
| Keyword:
|
Cartan geometry |
| Keyword:
|
almost complex structure |
| Keyword:
|
projective structure |
| MSC:
|
53B10 |
| MSC:
|
53C15 |
| idZBL:
|
Zbl 1212.53022 |
| idMR:
|
MR2591680 |
| . |
| Date available:
|
2009-12-22T07:52:48Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137458 |
| . |
| Reference:
|
[1] Čap, A., Slovák, J.: Weyl structures for parabolic geometries.Math. Scand. 93 (2003), 53–90. Zbl 1076.53029, MR 1997873 |
| Reference:
|
[2] Čap, A., Slovák, J.: Parabolic geometries I, Background and general theory.Math. Surveys Monogr., vol. 154, AMS Publishing House, 2009, p. 628. Zbl 1183.53002, MR 2532439 |
| Reference:
|
[3] Hrdina, J., Slovák, J.: Generalized planar curves and quaternionic geometry.Global analysis and geometry 29 (2006), 349–360. Zbl 1097.53008, MR 2251428 |
| Reference:
|
[4] Hrdina, J., Slovák, J.: Morphisms of almost product projective geometries.Differential Geometry and Applications, World Scientific, 2008, pp. 243–251. Zbl 1168.53013, MR 2462798 |
| Reference:
|
[5] Kobayashi, S.: Transformation groups in differential geometry.Springer-Verlag, New York-Heidelberg, 1972. Zbl 0246.53031, MR 0355886 |
| Reference:
|
[6] Mikeš, J., Sinyukov, N. S.: On quasiplanar mappings of spaces of affine connection.Soviet Math. 27 (1) (1983), 63–70. |
| Reference:
|
[7] Šilhan, J.: Algorithmic computations of Lie algebras cohomologies.Rend. Circ. Mat. Palermo (2) Suppl. 71 (2003), 191–197, Proceedings of the 22nd Winter School “Geometry and Physics” (Srní, 2002), www.math.muni.cz/ silhan/lie. Zbl 1032.17037, MR 1982446 |
| Reference:
|
[8] Yano, K.: Differential geometry on complex and almost complex spaces.The Macmillan Company NY, 1965. Zbl 0127.12405, MR 0187181 |
| . |
