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It is well-known that the unit cotangent bundle of any Riemann-ian manifold has a canonical contact structure. A surface in a Riemannian 3-manifold is called a (wave) front if it is the projection of a Legendrian immersion into the unit cotangent bundle. We shall give easily-computable criteria for a singular point on a front to be a cuspidal edge or aâ€¦ (More)

We shall introduce the singular curvature function on cuspidal edges of surfaces, which is related to the Gauss-Bonnet formula and which characterizes the shape of cuspidal edges. Moreover, it is deeply related to the behavior of the Gaussian curvature of a surface near cuspidal edges and swallowtails. Introduction LetM be an oriented 2-manifold and f : M â†’â€¦ (More)

We shall give a simple criterion for a given singular point on a surface to be a cuspidal cross cap. As an application, we show that the singularities of spacelike maximal surfaces in Lorentz-Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in deâ€¦ (More)

The hyperbolic Schwarz map is defined in [SYY1] as a map from the complex projective line to the three-dimensional real hyperbolic space by use of solutions of the hypergeometric differential equation. Its image is a flat front ([GMM, KUY, KRSUY]), and generic singularities are cuspidal edges and swallowtail singularities. In this paper, we studyâ€¦ (More)

- Elamurugu Elangovan, Kentaro Saji, +4 authors Elvira Fortunato
- IEEE Electron Device Letters
- 2011

Thin-film transistors (TFTs) were fabricated using a 20-nm-thick indium molybdenum oxide (IMO) semiconductor layer at room temperature. The grazing incidence x-ray diffraction patterns confirmed that the deposited films are amorphous. The average transmittance (400-2500 nm) and the optical band gap are ~ 88% and 3.95 eV, respectively. The TFTs fabricated onâ€¦ (More)

It is well-known that the unit cotangent bundle of any Riemann-ian manifold has a canonical contact structure. A surface in a Riemannian 3-manifold is called a (wave) front if it is the projection of a Legendrian immersion into the unit cotangent bundle. We shall give easily-computable criteria for a singular point on a front to be a cuspidal edge or aâ€¦ (More)

- Kentaro Saji
- 2009

The main objective of this paper is to study the identification problem of map germs. It means that for a given map germ on the classification table, finding simple criteria which will describe which germ on the table a given germ is equivalent to. The classification problem and recognition problem for map germs from the plane into the plane with respect toâ€¦ (More)

- Kentaro Saji
- 2009

In this paper, we give useful and easy computable criteria for D 4 singularities of wave front surfaces. As an application, we study behaviors of singular curvatures of cuspidal edge which incident a D 4 singularity.

It is well-known that the unit cotangent bundle of any Riemann-ian manifold has a canonical contact structure. A surface in a Riemannian 3-manifold is called a (wave) front if it is the projection of a Legendrian immersion into the unit cotangent bundle. We shall give easily-computable criteria for a singular point on a front to be a cuspidal edge or aâ€¦ (More)