6 papers · 1 filter
Surfaces of revolution of frontals in the Euclidean space
Masatomo Takahashi, Keisuke Teramoto
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 b…
Mixed type surfaces with bounded Gaussian curvature in three-dimensional Lorentzian manifolds
Atsufumi Honda, Kentaro Saji, Keisuke Teramoto
A mixed type surface is a connected regular surface in a Lorentzian 3-manifold with non-empty spacelike and timelike point sets. The induced metric of a mixed type surface is a sig…
Singularities of Gauss maps of wave fronts with non-degenerate singular points
Keisuke Teramoto
We study singularities of Gauss maps of fronts and give characterizations of types of singularities of Gauss maps by geometric properties of fronts which are related to behavior of…
Dualities of differential geometric invariants on cuspidal edges on flat fronts in the hyperbolic space and the de Sitter space
Kentaro Saji, Keisuke Teramoto
We compute the differential geometric invariants of cuspidal edges on flat surfaces in hyperbolic -space and in de Sitter space. Several dualities of invariants are pointed out.
Focal surfaces of wave fronts in the Euclidean 3-space
Keisuke Teramoto
We characterize singularities of focal surfaces of wave fronts in terms of differential geometric properties of the initial wave fronts. Moreover, we study relationships between ge…
Singularities of a surface given by Kenmotsu-type formula in Euclidean three-space
Luciana F. Martins, Kentaro Saji, Keisuke Teramoto
We study singularities of surfaces which are given by Kenmotsu-type formula with prescribed unbounded mean curvature.