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arXiv · 1009.6214

On the Local Isometric Embedding in R^3 of Surfaces with Gaussian Curvature of Mixed Sign

Qing Han·Marcus Khuri
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Abstract

We study the old problem of isometrically embedding a 2-dimensional Riemannian manifold into Euclidean 3-space. It is shown that if the Gaussian curvature vanishes to finite order and its zero set consists of two Lipschitz curves intersecting transversely at a point, then local sufficiently smooth isometric embeddings exist.

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Qing Han, Marcus Khuri. 2010-09-30. On the Local Isometric Embedding in R^3 of Surfaces with Gaussian Curvature of Mixed Sign. https://arxiv.org/abs/1009.6214

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