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The Semi-global Isometric Imbedding in R3 of Two Dimensional Riemannian Manifolds with Gaussian Curvature Changing Sign Cleanly
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@Article{JPDE-6-62,
author = {Dong Guangchang},
title = {The Semi-global Isometric Imbedding in R3 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&Pi] × [-&delta, &delta] where E, F, G are smooth functions of (u, v) and periodic in u with period 2&Pi. Moneover K|_{v=0} = 0. K_r|_{v=0} ≠ 0. when> 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}
}
TY - JOUR
T1 - The Semi-global Isometric Imbedding in R3 of Two Dimensional Riemannian Manifolds with Gaussian Curvature Changing Sign Cleanly
AU - Dong Guangchang
JO - Journal of Partial Differential Equations
VL - 1
SP - 62
EP - 79
PY - 1993
DA - 1993/06
SN - 6
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5700.html
KW -
AB - An abstract Riemannian metric ds²= Edu² + 2Fdudv + Gdv² is given in (u, v) ∈ [0, 2&Pi] × [-&delta, &delta] where E, F, G are smooth functions of (u, v) and periodic in u with period 2&Pi. Moneover K|_{v=0} = 0. K_r|_{v=0} ≠ 0. when> 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.
Dong Guangchang. (1993). The Semi-global Isometric Imbedding in R3 of Two Dimensional Riemannian Manifolds with Gaussian Curvature Changing Sign Cleanly.
Journal of Partial Differential Equations. 6 (1).
62-79.
doi:
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