  We describe the ${\cal{O}}({\alpha'}^0)$ constraints on the target space
geometry of the $N=(2,1)$ heterotic superstring due to the left-moving $N=1$
supersymmetry and $U(1)$ currents. In the fermionic description of the internal
sector supersymmetry is realized quantum mechanically, so that both tree-level
and one-loop effects contribute to the order ${\cal{O}}({\alpha'}^0)$
constraints. We also discuss the physical interpretation of the resulting
target space geometry in terms of configurations of a $2+2$-dimensional object
propagating in a $10+2$-dimensional spacetime with a null isometry, which has
recently been suggested as a unified description of string and M theory.
