| Title:
|
Yang-Mills bar connections over compact Kähler manifolds (English) |
| Author:
|
Vân Lê, Hông |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
47-69 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we introduce a Yang-Mills bar equation on complex vector bundles $E$ provided with a Hermitian metric over compact Hermitian manifolds. According to the Koszul-Malgrange criterion any holomorphic structure on $E$ can be seen as a solution to this equation. We show the existence of a non-trivial solution to this equation over compact Kähler manifolds as well as a short time existence of a related negative Yang-Mills bar gradient flow. We also show a rigidity of holomorphic connections among a class of Yang-Mills bar connections over compact Käahler manifolds of positive Ricci curvature. (English) |
| Keyword:
|
Kähler manifold |
| Keyword:
|
complex vector bundle |
| Keyword:
|
holomorphic connection |
| Keyword:
|
Yang-Mills bar gradient flow |
| MSC:
|
53C44 |
| MSC:
|
53C55 |
| MSC:
|
58E99 |
| idZBL:
|
Zbl 1240.53118 |
| idMR:
|
MR2644454 |
| . |
| Date available:
|
2010-04-22T10:43:30Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/139995 |
| . |
| Reference:
|
[1] Bourguignon, J. P., Lawson, H. B.: Stability phenomena for Yang-Mills fields.Commun. Math. Phys. 79 (1981), 189–230. MR 0612248, 10.1007/BF01942061 |
| Reference:
|
[2] Donaldson, S. K., Kronheimer, P. B.: The geometry of 4-manifolds.Clarendon Press, Oxford, 1990. MR 1079726 |
| Reference:
|
[3] Griffiths, P., Harris, J.: Principles of algebraic geometry.2nd ed., Wiley Classics Library, New York, 1994. Zbl 0836.14001, MR 1288523 |
| Reference:
|
[4] Hamilton, R.: Three manifold with positive Ricci curvature.J. Differential Geom. 17 (2) (1982), 255–306. MR 0664497 |
| Reference:
|
[5] Kobayashi, S.: Differential geometry of complex vector bundles.Iwanami Shoten Publishers and Princeton University Press, 1987. Zbl 0708.53002, MR 0909698 |
| Reference:
|
[6] Koszul, J. L., Malgrange, B.: Sur certaines structures fibres complexes.Arch. Math. (Basel) 9 (1958), 102–109. MR 0131882, 10.1007/BF02287068 |
| . |
