Osculating spheres and osculating circles of a curve in semi-riemannian space

The Osculating Plane of a Space Curve - Synthetic Formulations

Rotation-minimizing osculating frames

An orthonormal frame (f1, f2, f3) is rotation–minimizing with respect to fi if its angular velocity ω satisfies ω · fi ≡ 0 — or, equivalently, the derivatives of fj and fk are both parallel to fi. The Frenet frame (t,p,b) along a space curve is rotation–minimizing with respect to the principal normal p, and in recent years adapted frames that are rotation–minimizing with respect to the tangent ...

Osculating Paths and Oscillating Tableaux

The combinatorics of certain tuples of osculating lattice paths is studied, and a relationship with oscillating tableaux is obtained. The paths being considered have fixed start and end points on respectively the lower and right boundaries of a rectangle in the square lattice, each path can take only unit steps rightwards or upwards, and two different paths within a tuple are permitted to share...

Lines and Osculating Lines of Hypersurfaces

This is a detailed study of the infinitesimal variation of the varieties of lines and osculating lines through a point of a low degree hypersurface in projective space. The motion is governed by a system of partial differential equations which we describe explicitly.

Osculating Random Walks on Cylinders

We consider random paths on a square lattice which take a left or a right turn at every vertex. The possible turns are taken with equal probability, except at a vertex which has been visited before. In such case the vertex is left via the unused edge. When the initial edge is reached the path is considered completed. We also consider families of such paths which together cover every edge of the...