The flat torus in is defined as the isometric direct product of two circles of equal radius, embedded in orthogonal s.
Consider with coordinates . The flat torus obtained by taking the direct product of the unit circle is the -plane and the unit circle in the plane is defined as the set of points satisfying the following two equations:
The flat torus has zero sectional curvature, on account of being a direct product of two curves. In fact, any surface in obtained as an isometric direct product of a curve in and a curve in , has zero sectional curvature. Template:Justify