Isometric immersions of Euclidean plane into Euclidean 4-space with vanishing normal curvature
Mori, Hiroshi ; Shimakura, Norio
Tohoku Math. J. (2), Tome 61 (2009) no. 1, p. 523-550 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 2009-05-15
Classification:  Isometric immersions,  structure equations,  Goursat problem,  asymptotic analysis,  53C42,  35L70 
@article{1264084498,
     author = {Mori, Hiroshi and Shimakura, Norio},
     title = {Isometric immersions of Euclidean plane into Euclidean 4-space with vanishing
				normal curvature},
     journal = {Tohoku Math. J. (2)},
     volume = {61},
     number = {1},
     year = {2009},
     pages = { 523-550},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1264084498}
}

Mori, Hiroshi; Shimakura, Norio. Isometric immersions of Euclidean plane into Euclidean 4-space with vanishing
				normal curvature. Tohoku Math. J. (2), Tome 61 (2009) no. 1, pp.  523-550. http://gdmltest.u-ga.fr/item/1264084498/