If the $S^1$ is defined by $x^2 + y^2 = r^2$ ,
$T^2 = S^1 \times S^1$ is defined by $\left(\sqrt{x^2 + y^2} -R\right)^2 + z^2 = r^2$ ,
$T^3=S^1\times S^1\times S^1$ is defined by $\left(\sqrt{\left(\sqrt{x^2 + y^2} -R_1\right)^2 + z^2} -R_2\right)^2 + w^2 = r^2$,
then what notation can we use to represent
$$\left(\sqrt{x^2 + y^2} -R_a\right)^2 + \left(\sqrt{z^2 + w^2} -R_b\right)^2 = r^2$$
which is a circle-bundle over a flat 2-torus (cartesian product of 2 orthogonal circles) ? Something in the form $S^1\times\cdots\,{}$?