Classification of surfaces with pointwise planar normal sections and its application to Fomenko's conjecture
Let \(\gamma\) be the intersection curve of a surface M in \(E^ m\) with a hyperplane H continuing the normal space of M at \(p\in M\). If the first 3 derivatives of \(\gamma\) are linearly dependent for each choice of p and H, then M has pointwise planar normal sections. The authors show that then M is either locally in \(E^ 3\) or an open portion of a Veronese surface in \(E^ 5\) or a standard torus \(S^ 1\times S^ 1\) in \(E^ 4\).
scientific article; zbMATH DE number 3942368
scientific article