On singularities of submanifolds of higher dimensional Euclidean spaces

Summary Generalizations of principle axes are found for surfaces in E⁴. The singularities generalize umbilics. The generic indicies are computed. For these computations the Thom Transversality Theorem as applied by Feldman to geometry is used. Hower we ? reduce the group ? rendering the calculations more tractible. Also we show that a torus or sphere cannot be immersed in E⁴ with everywhere nonzero curvature of the normal bundle. Entrata in Redazione il 19 novembre 1968.