Abstract
Every isometric immersion of ${\boldsymbol R}^2$ into ${\boldsymbol R}^4$ with vanishing normal curvature is assosiated with a pair of real-valued functions satisfying a system of second order partial differential equations of hyperbolic type,and vice versa. An isometric immersion with vanishing normal curvature is revealed to be multiple-valued in general as is shown by some concrete examples.
Citation
Hiroshi Mori. Norio Shimakura. "Isometric immersions of Euclidean plane into Euclidean 4-space with vanishing normal curvature." Tohoku Math. J. (2) 61 (4) 523 - 550, 2009. https://doi.org/10.2748/tmj/1264084498
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