Tohoku Mathematical Journal

Numerically flat principal bundles

Indranil Biswas and Swaminathan Subramanian

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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 $\text{ad}(E_G)$ is numerically flat. Numerically flat bundles are also characterized using the notion of semistability.

Article information

Source
Tohoku Math. J. (2), Volume 57, Number 1 (2005), 53-63.

Dates
First available in Project Euclid: 11 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1113234834

Digital Object Identifier
doi:10.2748/tmj/1113234834

Mathematical Reviews number (MathSciNet)
MR2113990

Zentralblatt MATH identifier
1072.32010

Subjects
Primary: 32L05: Holomorphic bundles and generalizations
Secondary: 53C05: Connections, general theory

Keywords
Principal bundle numerically flat bundle Kähler manifold

Citation

Biswas, Indranil; Subramanian, Swaminathan. Numerically flat principal bundles. Tohoku Math. J. (2) 57 (2005), no. 1, 53--63. doi:10.2748/tmj/1113234834. https://projecteuclid.org/euclid.tmj/1113234834


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