Preprints related to Special Holonomy
(or whatever else seems interesting to the Special Holonomy RAP group)

Atiyah, M., Maldacena, J., Vafa, C. : An M-theory Flop as a Large N Duality
Journal-ref: J.Math.Phys. 42 (2001) 3209-3220 [hep-th/0011256 ]

Atiyah, M. and Witten, E.: M-Theory Dynamics On A Manifold Of G_2 Holonomy
[hep-th/0107177 ]

Hitchin, N.: Generalized Calabi-Yau manifolds
[math.DG/0209099]
 A geometrical structure on even-dimensional manifolds is defined which
 generalizes the notion of a Calabi-Yau manifold and also a symplectic
 manifold. Such structures are of either odd or even type and can be transformed by the
 action of both diffeomorphisms and closed 2-forms. In the special case of
 six dimensions we characterize them as critical points of a natural variational
 problem on closed forms, and prove that a local moduli space is provided by
 an open set in either the odd or even cohomology.

Robert L. Bryant  Some remarks on G_2-structures
[math.DG/0305124]

This article consists of some loosely related remarks about the geometry of
G_2-structures on 7-manifolds and is based on old unpublished joint work with
two other people: F. Reese Harvey and Steven Altschuler. Much of this work has
since been subsumed in the work of Hitchin \cite{MR02m:53070} and
Joyce \cite{MR01k:53093}. I am making it available now mainly because of
interest expressed by others in seeing these results written up since they do
not seem to have all made it into the literature.
  A formula is derived for the scalar curvature and Ricci curvature of a
G_2-structure in terms of its torsion. When the fundamental 3-form of the
G_2-structure is closed, this formula implies, in particular, that the scalar
curvature of the underlying metric is nonpositive and vanishes if and only if
the structure is torsion-free.
  Some formulae are derived for closed solutions of the Laplacian flow that
specify how various related quantities, such as the torsion and the metric,
evolve with the flow. These may be useful in studying convergence or long-time
existence for given initial data.

(added May 9,2003)

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Last updated September 16, 2002