**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** S*ome 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G_2-structures on 7-manifolds and is based on old unpublished joint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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