## Tohoku Mathematical Journal 2005 March SECOND SERIES VOL. 57, NO. 1

 Tohoku Math. J. 57 (2005), 53-63

Title NUMERICALLY FLAT PRINCIPAL BUNDLES

Author Indranil Biswas and Swaminathan Subramanian

(Received May 12, 2003, revised July 29, 2004)
Abstract. 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 $\mathrm{ad}(E_G)$ is numerically flat. Numerically flat bundles are also characterized using the notion of semistability.

2000 Mathematics Subject Classification. Primary 32L05; Secondary 53C05.

Key words and phrases. Principal bundle, numerically flat bundle, Kähler manifold.