On the Cylinder Theorem in $M^2\times {\mathbb{R}}^n$

Abstract

Consider a surface $M^2$ with Gaussian curvature either $<0$ or $>0$. We prove that in $M^2\times {\mathbb{R}}^n$ cylinders are characterized as the hypersurfaces with both the extrinsic and intrinsic curvatures equal to zero.

11 pages