On the Gauss equation of an isometric immersion
The authors investigate the algebraic problem to represent a curvature like tensor R (on an n-dimensional linear space) by the right side of Gauß equation (of submanifolds in Euclidean space) involving the least possible number cl(R) of symmetric bilinear forms. They give a constructive proof for \(cl(R)\leq\binom{n}{2}\). In fact, \(cl(R)\leq\binom{n}{2}-(n-3)\) [cf. \textit{E. Berger, R. Bryant} and \textit{P. Griffiths}, Duke Math. J. 50, 803-892 (1983; Zbl 0526.53018)]. The authors prove the usefulness of their method by using it to derive again several well-known facts, for instance the Allendoerfer-Chern ''type number and rigidity'' theorem.
scientific article; zbMATH DE number 3868143
scientific article