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A relation between the right triangle and circular tori with constant mean curvature in the unit 3-sphere

In this note we will show that the inverse image under the stereographic projection of a circular torus of revolution in the 3-dimensional euclidean space has constant mean curvature in the unit 3-sphere if and only if their radii are the catet and the hypotenuse of an appropriate right triangle.

Flat torus; constant mean curvature; circular tori; stereographic projection


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