Small parameter in the theory of isometric imbeddings for two-dimensional Riemannian manifolds into Euclidean spaces
The article presents a survey of research papers of the authors and of J. Kajdasov, C. S. Lin, G. Nakamura, B. L. Rozhdestvenskij, D. V. Tunitskij a.o. Chapter headings are: 1. Numerical parameter in the isometric imbedding problems of the negative-curvature manifolds into the Euclidean space \(E^3\). 2. A small functional parameter in the imbedding problems of manifolds with negative curvature. 3. A small parameter in the sine-Gordon equation. 4. The isometric imbedding of two-dimensional manifolds into the four-dimensional Euclidean space. 5. A small parameter in the isometric imbedding problems for analytic metrics. 6. Application of a small parameter for the imbedding of two-dimensional manifolds of curvature with alternating signs.
isometric imbedding into Euclidean space
scientific article; zbMATH DE number 877643
scientific article