Math @ Duke

Publications [#318281] of Robert Bryant
search www.ams.org.Papers Published
 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. 505514, American Mathematical Society, ISBN 0821801104 [MR89f:53068]
(last updated on 2017/12/12)
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This paper has since been superceded by S.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 G_{2}
or Spin(7). Considerably more is now known about the
geometry of the socalled
quaternionicKähler manifolds. The works of
Joyce, Salamon, and LeBrun
should be consulted for further information on these
subjects.


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