New Flat surfaces in $S^3$

Published 8 Mar 2021 in math.GT | (2103.04679v1)

Abstract: n this paper, we consider a method of constructing flat surfaces based on Ribaucour transformations in the sphere 3-space. By applying the theory to the flat torus, we obtain a families of complete flat surfaces in $S^3$ which are determined by several parameters. we provide explicit examples.

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