Locally Euclidean metrics and their isometric realizations

DOI10.1007/s10958-023-06802-6OpenAlexW4389088444MaRDI QIDQ6147673

Idzhad Kh. Sabitov

Publication date: 1 February 2024

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-023-06802-6

zbMATH Keywords

developable surfacesasymptotic coordinateslocally Euclidean metrics

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Local Riemannian geometry (53B20)

Cites Work

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• Isometric embeddings in \(\mathbb{R}^3\) of an annulus with a locally Euclidean metric which are multivalued of cylindrical type
• Entire solutions of the degenerate Monge-Ampère equation with a finite number of singularities
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• The explicit general solution of trivial Monge-Ampère equation
• Isometric embeddings of locally Euclidean metrics in \(\mathbb R^3\) as conical surfaces
• Solutions of the trivial Monge-Ampère equation with isolated singular points
• On the smoothness of isometries
• On Spherical Image Maps Whose Jacobians Do Not Change Sign
• Partial Differential Relations
• Parameterisation of developable surfaces by asymptotic lines
• Isometric immersions and embeddings of locally Euclidean metrics in $ \mathbb R^2$
• Isometric immersions and embeddings of a flat Möbius strip in Euclidean spaces

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