Difference between revisions of "Flat torus"
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Latest revision as of 19:40, 18 May 2008
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