Surfaces of Revolution of Frontals in the Euclidean Space

Abstract

For Legendre curves, we consider surfaces of revolution of frontals. The surface of revolution of a frontal can be considered as a framed base surface. We give the curvatures and basic invariants for surfaces of revolution by using the curvatures of Legendre curves. Moreover, we give properties of surfaces of revolution with singularities and cones.2010 Mathematics Subject classification: 57R45, 53A05, 58K05

Boundedness of geometric invariants near a singularity which is a suspension of a singular curve

“…If a surface is invariant under a group action on R 3 , then σ-edges will appear naturally. Singularities appearing on surfaces of revolution and a helicoidal surface are examples of such surfaces [10,13]. Moreover, such singularities appear on the dual surface at cone like singular points of a constant mean curvature one surface in the de Sitter 3-space (see [6]).…”