Is the maximal complex subtorus in real torus dense?

67 Views Asked by At

Consider the torus $\mathbb R^3/\mathbb Z^3$. Then the maximal complex subgroup is $\mathbb R^2/\mathbb Z^2$. Right?

Is $\mathbb R^2/\mathbb Z^2$ dense in $\mathbb R^3/\mathbb Z^3$?