Flat torus
Definition
The flat torus in is defined as the isometric direct product of two circles of equal radius, embedded in orthogonal
s.
Equational description
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:
Curvature
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