  A compact four-dimensional manifold whose metric tensor has a positive
determinant (named the "Euclid ball") is considered. The Euclid ball can be
immersed in the Minkovskian space (which has the negative determinant) and can
exist stably through the history of the universe. Since the Euclid ball has the
same solution as the Schwarzschild black hole on its three-dimensional surface,
an asymptotic observer can not distinguish them. If large fraction of whole
energy of the pre-universe was encapsulated in Euclid balls, they behave as the
dark matter in the current universe. Euclid balls already existed at the end of
the cosmological inflation, and can have a heavy mass in this model, they can
be a seed of supper-massive black-holes, which are necessary to initiate a
forming of galaxies in the early universe. The $\gamma$-ray burst at early
universe is also a possible signal of the Euclidean ball.
