TITLE:
Helicoidal Surfaces and Their Relationship to Bonnet Surfaces
AUTHORS:
Paul Bracken
KEYWORDS:
Surface, Fundamental Forms, Structure Equations, Mean Curvature, Bonnet, Helicoidal
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.7 No.1,
January
24,
2017
ABSTRACT: An important question that arises is which surfaces in three-space admit a mean curvature preserving isometry which is not an isometry of the whole space. This leads to a class of surface known as a Bonnet surface in which the number of noncongruent immersions is two or infinity. The intention here is to present a proof of a theorem using an approach which is based on differential forms and moving frames and states that helicoidal surfaces necessarily fall into the class of Bonnet surfaces. Some other results are developed in the same manner.