42 citations · 78 across the 18 of their papers we have counts for
18 papers
Focal surfaces of fronts associated to unbounded principal curvatures
Keisuke Teramoto
We study focal surfaces of (wave) fronts associated to unbounded principal curvatures near non-degenerate singular points of initial fronts. We give characterizations of singularit…
On surfaces obtained as singular loci of normal congruences of frontals with pure-frontal singular points
Samuel P. dos Santos, Keisuke Teramoto
We study singularities and geometric properties of surfaces given by the singular loci of normal congruence of frontals with pure-frontal singular points. These surfaces consist of…
Boundedness of geometric invariants near a singularity which is a suspension of a singular curve
Luciana F. Martins, Kentaro Saji, Samuel P. dos Santos +1
Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of diverge, in particular the boundedness about these invariants represent ge…
Geometry of lightlike locus on mixed type surfaces in Lorentz-Minkowski 3-space from a contact viewpoint
Atsufumi Honda, Shyuichi Izumiya, Kentaro Saji +1
A surface in the Lorentz-Minkowski -space is generally a mixed type surface, namely, it has the lightlike locus. We study local differential geometric properties of such a locus…
On Gaussian curvatures and singularities of Gauss maps of cuspidal edges
Keisuke Teramoto
We show relation between sign of Gaussian curvature of cuspidal edge and geometric invariants through types of singularities of Gauss map. Moreover, we define and characterize posi…
Geometric properties near singular points of surfaces given by certain representation formulae
Yoshiki Matsushita, Takuya Nakashima, Keisuke Teramoto
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces alo…
Behavior of principal curvatures of frontals near non-front singular points and their application
Kentaro Saji, Keisuke Teramoto
We investigate behavior of principal curvatures and principal vectors near a non-degenerate singular point of the first kind of frontals. As an application, we extend the notion of…
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.
Singular surfaces of revolution with prescribed unbounded mean curvature
Luciana F. Martins, Kentaro Saji, Samuel P. dos Santos +1
We give an explicit formula for singular surfaces of revolution with prescribed unbounded mean curvature. Using it, we give conditions for singularities of that surfaces. Periodici…
Flat surfaces along swallowtails
Shyuichi Izumiya, Kentaro Saji, Keisuke Teramoto
We consider developable surfaces along the singular set of a swallowtail which are considered to be flat approximations of the swallowtail. For the study of singularities of such d…
Characterizing singularities of a surface in Lie sphere geometry
Mason Pember, Wayne Rossman, Kentaro Saji +1
The conditions for a cuspidal edge, swallowtail and other fundamental singularities are given in the context of Lie sphere geometry. We then use these conditions to study the Lie s…
Principal curvatures and parallel surfaces of wave fronts
Keisuke Teramoto
We give criteria for which a principal curvature becomes a bounded -function at non-degenerate singular points of wave fronts by using geometric invariants. As applicatio…
Parallel and dual surfaces of cuspidal edges
Keisuke Teramoto
We study parallel surfaces and dual surfaces of cuspidal edges. We give concrete forms of principal curvature and principal direction for cuspidal edges. Moreover, we define ridge…