  We study finitely generated projective modules over noncommutative tori. We
prove that for every module $E$ with constant curvature connection the
corresponding element $[E]$ of the K-group is a generalized quadratic exponent
and, conversely, for every positive generalized quadratic exponent $\mu$ in the
K-group one can find such a module $E$ with constant curvature connection that
$[E] = \mu $. In physical words we give necessary and sufficient conditions for
existence of 1/2 BPS states in terms of topological numbers.
