  We proved that under quantum mechanics a momentum-energy and a space-time are
dual vector spaces on an almost complex manifold in position representation,
and the minimal uncertainty relations are equivalent to the inner-product
relations of their bases. In a microscopic sense, there exist locally a
momentum-energy conservation and a space-time conservation. The minimal
uncertainty relations refer to a local equilibrium state for a stable system,
and the relations will be invariable in the special relativity. A supposition
about something having dark property is proposed, which relates to a breakdown
of time symmetry.
