Generalizing the notion of a numerically flat vector bundle over a Kähler manifold $M$, we define a numerically flat principal $G$-bundle over $M$, where $G$ is a semisimple complex algebraic group. It is proved that a principal $G$-bundle $E_G$ is numerically flat if and only if $\text{ad}(E_G)$ is numerically flat. Numerically flat bundles are also characterized using the notion of semistability.
Publié le : 2005-03-14
Classification:
Principal bundle,
numerically flat bundle,
Kähler manifold,
32L05,
53C05
@article{1113234834,
author = {Biswas, Indranil and Subramanian, Swaminathan},
title = {Numerically flat principal bundles},
journal = {Tohoku Math. J. (2)},
volume = {57},
number = {1},
year = {2005},
pages = { 53-63},
language = {en},
url = {http://dml.mathdoc.fr/item/1113234834}
}
Biswas, Indranil; Subramanian, Swaminathan. Numerically flat principal bundles. Tohoku Math. J. (2), Tome 57 (2005) no. 1, pp. 53-63. http://gdmltest.u-ga.fr/item/1113234834/