Surfaces of 𝐸⁴ satisfying certain restrictions on their normal bundle

Abstract

We consider smooth surfaces in E 4 {E^4} whose normal bundles satisfy certain geometric conditions that entail the vanishing of the normal curvature, and prove that their Gauss curvatures cannot be bounded from above by a negative number. We also give some results towards a classification of flat surfaces with flat normal bundle in E 4 {E^4} .