Lightlike surfaces of spacelike curves in de Sitter 3-space

The Lorentzian space form with the positive curvature is called de Sitter space which is an important subject in the theory of relativity. In this paper we consider spacelike curves in de Sitter 3-space. We define the notion of lightlike surfaces of spacelike curves in de Sitter 3-space. We investigate the geometric meanings of the singularities of such surfaces. Work partially supported by Grant-in-Aid for formation of COE. ‘Mathematics of Nonlinear Structure via Singularities’     

Lightcone dualities for hypersurfaces in the sphere

In this paper, we consider hypersurfaces in the unit lightlike sphere. The unit sphere can be canonically embedded in the lightcone and de Sitter space in Minkowski space. We investigate these hypersurfaces in the framework of the theory of Legendrian dualities between pseudo‐spheres in Minkowski space.     

Efficient asymmetric synthesis of α-amino acids through hydrogenation of α,β-dehydroamino acid residue in cyclic dipeptides

A series of cyclo (Δaminoacyl-L-Ala) ($\text{4}$) (Δ=α,β-dehydro) were prepared from cyclo(Gly-L-Ala) and corresponding aldehyde, and hydrogenated with Pd black in MeOH. Chiral inductions producing cyclo (L-aminoacyl-L-Ala) ($\text{5}$) from $\text{4}$ were 96–99% in the case of L-Aba (2-aminobutanoic acid), L-Val, L-Leu, and L-App (2-amino-5-phenylpentanoic acid) as an L-aminoacyl moiety in $\text{5}$. Pure L-Leu, L-Aba, and L-App were synthesized in preparative scale from corresponding $\text{4}$ through asymmetric hydrogenation and acid-hydrolysis.     

A time-like surface in Minkowski 3-space which contains light-like lines

Simple characterizations of a pseudosphere or a time-like plane in Minkowski 3-space by the existence of light-like lines are given.     

Great circular surfaces in the three-sphere

In this paper, we consider a special class of the surfaces in the 3-sphere defined by one-parameter families of great circles. We give a generic classification of singularities of such surfaces and investigate the geometric meanings from the view point of spherical geometry.     

Anti de Sitter horospherical flat timelike surfaces

We investigate a special timelike surfaces in Anti de Sitter 3-space.We call such a timelike surface an Anti de Sitter horospherical flat surface which belongs to a class of surfaces given by one parameter families of Anti de Sitter horocycle.We give a generic classification of singularities and study the geometric properties of such surfaces from the viewpoint of Legendrian singularity theory.