Degenerate conics revisited

Degenerate torsion-free G3-connections revisited

between any two coordinates ( i) and ( i). Hence any choice of Γ k ij in one coordinate chart suffices to define the connection in another. Let T k ij := Γkij − Γkji be the torsion tensor of the connection. The case when torsion is zero (torsion-free) is of particular interest in geometry. In Hermann Weyl’s terms [11], the very existence of inertia systems in the Universe warrants that its line...

The projective reconstruction of points, lines, quadrics, plane conics and degenerate quadrics using uncalibrated cameras

In this paper we present an algorithm for the simultaneous projective reconstruction of points, lines, quadrics, plane conics and degenerate quadrics using Bundle Adjustment. In contrast, most existing work on projective reconstruction focuses mainly on one type of primitive. Furthermore, for the reconstruction of quadrics (both full-rank and degenerate) and plane conics, a novel algorithm for ...

Rational Points on Pencils of Conics and Quadrics with Many Degenerate Fibres

For any pencil of conics or higher-dimensional quadrics over Q, with all degenerate fibres defined over Q, we show that the Brauer–Manin obstruction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics over Q, which is a consequence of recent advances in additive combinatorics.

Discrete Conics

In this paper, we introduce discrete conics, polygonal analogues of conics. We show that discrete conics satisfy a number of nice properties analogous to those of conics, and arise naturally from several constructions, including the discrete negative pedal construction and an action of a group acting on a focus-sharing pencil of conics.

Liquids with conics