Recent advances in the theory of holonomy


Journal Article

After its introduction by Élie Cartan, the notion of holonomy has become increasingly important in Riemannian and affine geometry. Beginning with the fundamental work of Marcel Berger, the classification of possible holonomy groups of torsion free connections, either Riemannian or affine, has continued to be developed, with major breakthroughs in the last ten years. I will report on the local classification in the affine case, Joyce's fundamental work on compact manifolds with exceptional holonomies and their associated geometries, and some new work on the classification of holonomies of connections with restricted torsion, which has recently become of interest in string theory.

Full Text

Duke Authors

Cited Authors

  • Bryant, R

Published Date

  • December 1, 2000

Published In

Volume / Issue

  • 266 /

Start / End Page

  • 351 - 374

International Standard Serial Number (ISSN)

  • 0303-1179

Citation Source

  • Scopus