In the following we show the only possible flat, connected, incomplete homogeneous spacetimes are
H
/
Δ
H / \Delta
where
H
=
{
υ
∈
R
n
|
g
(
υ
,
N
)
>
0
}
,
N
H = \left \{ {\upsilon \in {{\mathbf {R}}^n}\left | {g\left ( {\upsilon ,N} \right ) > 0} \right .} \right \},N
is a null vector, and
Δ
\Delta
is a discrete subgroup of translations.