Isometric deformation of (m, n)-type helicoidal surface in the three dimensional euclidean space

Abstract

We consider a new kind of helicoidal surface for natural numbers (m, n) in the three-dimensional Euclidean space. We study a helicoidal surface of value (m, n), which is locally isometric to a rotational surface of value (m, n). In addition, we calculate the Laplace–Beltrami operator of the rotational surface of value (0, 1).