A D'Alembert Formula for Flat Surfaces in the 3-Sphere
2009 - J.A. Aledo. J.A. Gálvez, P. Mira
Journal of Geometric Analysis 19, 211-232 (2009)
authors IMACI
Abtract
We find all the flat surfaces in the unit 3-sphere S3 that pass through a given regular curve of S3 with a prescribed tangent plane distribution along this curve. The formula that solves this problem may be seen as a geometric analogue of the classical D’Alembert formula that solves the Cauchy problem for the homogeneous wave equation. We also provide several applications of this geometric D’Alembert formula, including a classification of the flat Möbius strips of S3