@Article{JPDE-6-62,
author = {Dong Guangchang},
title = {The Semi-global Isometric Imbedding in <em>R</em><sup>3</sup> of Two Dimensional Riemannian Manifolds with Gaussian Curvature Changing Sign Cleanly},
journal = {Journal of Partial Differential Equations},
year = {1993},
volume = {6},
number = {1},
pages = {62--79},
abstract = { An abstract Riemannian metric ds²= Edu² + 2Fdudv + Gdv² is given in (u, v) ∈ [0, 2&amp;Pi] × [-&amp;delta, &amp;delta] where E, F, G are smooth functions of (u, v) and periodic in u with period 2&amp;Pi. Moneover K|_{v=0} = 0. K_r|_{v=0} ≠ 0. when&gt; K is the Gaussian curvature. We imbed it semiglobally as the graph of a smooth surface x = x(u, v ), y = y(u, v), z = z(u, v) of R³ in the neighborhood of v = 0. In this paper we show that, if [K_rΓ²_{11}]_{v=0}, and three compatibility conditions are satisified, then there exists such an isometric imbedding.},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5700.html}
}