The Euler characteristic of a generic wave front in a 3‐manifold

We give a relation between Euler characteristics of a generic closed Legendrian surface and its wavefront

Singularities of ruled surfaces in R3

We study singularities of ruled surfaces in JR3. The main result asserts that only cross­caps appear as singularities for generic ruled surfaces

The Euler number of a topologically stable singular surface in a 3‐manifold

A formula for the Euler number of a generic singular surface in a 3-manifold is given. This formula not only unifies the previous results but also allows some new applications

Generic special curves

We study generic properties of cylindrical helices and Bertrand curves as applications of singularity theory for plane curves and spherical curves

New special curves and developable surfaces

We define new special curves in Euclidean 3-space which we call slant helices and conical geodesic curves. Those notions are generalizations of the notion of cylin­drical helices. One of the results in this paper gives a classification of special de­velopable surfaces under the condition of the existence of such a special curve as a geodesic. As a result, we consider geometric invariants of space curves. By using these invariants, we can estimate the order of contact with those special curves for general space curves. All arguments in this paper are elementary and classi­cal. However, there have been no papers which have investigated slant helices and conical geodesic curves so far as we know

Singularities of solution surfaces for quasilinear 1st order partial differential equations

We study singularities of solution surfaces of characteristic Cauchy problem for quasilinear first order partial differential equations as an application of the previous result on vector fields near a generic submanifold