  The idea of an oscillating Universe has remained a topic of interest even
after the discovery of dark energy. This paper confirms this idea by means of
another well-established theory in general relativity, the embedding of curved
spacetimes in higher-dimensional flat spacetimes: an $n$-dimensional Riemannian
space is said to be of embedding class $m$ if $m+n$ is the lowest dimension $d$
of the flat space in which the given space can be embedded; here
$d=\frac{1}{2}n(n-1)$. So a four-dimensional Riemannian space is of class two
since it can be embedded in a six-dimensional flat space. A line element of
class two can be reduced to a line element of class one by a suitable
coordinate transformation. The extra dimension can be either spacelike or
timelike, leading to accelerating and decelerating expansions, respectively.
Accordingly, it is proposed in this paper that the free parameter occurring in
the transformation be a periodic function of time. The result is a mathematical
model that can be interpreted as a periodic change in the signature of the
embedding space. This signature change may be the best model for an oscillating
Universe and complements various models proposed in the literature.
