New Flat Surfaces in S3 (Selecciones Matemáticas, 2021)
In this paper, we consider a method of constructing flat surfaces based on Ribaucour transformations in S3. By applying the theory to the flat torus, we obtain a family of complete flat surfaces in S3 which is determined by several parameters. We provide explicit examples.
Keywords: Flat surfaces; Ribaucour transformations; 3-sphere; flat torus; complete surface