Index of an implicit differential equation
In the first part of the article, the authors introduce the notion of an index of an implicit ordinary differential equation at an isolated singularity and show that equivalent germs of implicit differential equations possess identical indices. They provide explicit expressions for the case of binary differential equations of degree \(3\). In the second part, these results are applied to study surfaces embedded in \(I\!\!R^5\). An index is introduced for symmetric \(n\)-forms on a surface and related to the Poincaré-Hopf theorem.
scientific article; zbMATH DE number 5666218
scientific article