Publications [#318281] of Robert Bryant

Papers Published

1. Bryant, R, A survey of Riemannian metrics with special holonomy groups, in Proceedings of the International Congress of Mathematicians. Vol. 1, 2. (Berkeley, Calif., 1986), edited by Gleason, A (1987), pp. 505-514, American Mathematical Society, ISBN 0-8218-0110-4 [MR89f:53068]
   (last updated on 2025/02/21)

   Author's Comments:
   A survey paper that details what was known at the time about Riemannian metrics with reduced holonomy.

   This paper has since been superceded by S. Salamon's 1989 book on Riemannian geometry and holonomy. However both of these are now inadequate. The results of D. Joyce show that there exist compact manifolds with holonomy G₂ or Spin(7). Considerably more is now known about the geometry of the so-called quaternionic-Kähler manifolds. The works of Joyce, Salamon, and LeBrun should be consulted for further information on these subjects.