Immersions with circular normal sections and normal sections of product immersions (Q1074877)

An isometric immersion \(i: M\to E^ m\) is said to have circular normal sections if all normal sections are locally circles. It is said to have spherical k-normal sections \((k>1)\) if all k-normal sections are locally first standard imbedded spheres in \(E_ m\). In this article, the authors classify isometric immersions which have spherical k-normal sections. They obtain some lemmas concerning local sections of product immersions. As applications they determine all parallel immersions with planar normal sections and all immersions with planar normal sections and trivial normal connection.