On the perturbation problem associated to isometric embeddings of Riemannian manifolds
In the classical problem of isometric embedding of a Riemannian manifold into Euclidean space \({\mathbb{R}}^ q\) first, an ``almost'' isometric embedding is constructed, and then a special system of differential equations is solved for the ``correction'' term. The second step relies to the hard implicit function theorem (IFT) of Moser-Nash. In this article the author suggests a modified version of the system of equations for the ``correction'' term. For this system one can avoid using hard IFT.
scientific article; zbMATH DE number 4131176