<s>
In	O
mathematics	O
,	O
a	O
Spin(7 )	O
-manifold	O
is	O
an	O
eight-dimensional	O
Riemannian	B-Architecture
manifold	I-Architecture
whose	O
holonomy	O
group	O
is	O
contained	O
in	O
Spin(7 )	O
.	O
</s>
<s>
Spin(7 )	O
-manifolds	O
are	O
Ricci-flat	B-Algorithm
and	O
admit	O
a	O
parallel	O
spinor	O
.	O
</s>
<s>
if	O
such	O
a	O
manifold	O
did	O
in	O
fact	O
exist	O
,	O
it	O
would	O
carry	O
a	O
parallel	O
4-form	O
,	O
and	O
that	O
it	O
would	O
necessarily	O
be	O
Ricci-flat	B-Algorithm
.	O
</s>
