Isometric immersions of Euclidean plane into Euclidean 4-space with vanishing normal curvature
Hiroshi Mori and Norio Shimakura
Source: Tohoku Math. J. (2) Volume 61, Number 4
(2009), 523-550.
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.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.tmj/1264084498
Digital Object Identifier: doi:10.2748/tmj/1264084498
Zentralblatt MATH identifier: 05687942
Mathematical Reviews number (MathSciNet): MR2598248
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