Isometric Deformation of (<i>m</i>,<i>n</i>)-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 ) .

Keywords

• euclidean three-space
• helicoidal surface of value (<i>m</i>,<i>n</i>)
• rotational surface of value (<i>m</i>,<i>n</i>)
• mean curvature
• Gaussian curvature
• Gauss map