Congruences and Concurrent Lines in Multi-View Geometry

Metric and periodic lines in the Poincare ball model of hyperbolic geometry

In this paper, we prove that every metric line in the Poincare ball model of hyperbolic geometry is exactly a classical line of itself. We also proved nonexistence of periodic lines in the Poincare ball model of hyperbolic geometry.

Classification of Smooth Congruences with a Fundamental Curve

We give a classification and a construction of all smooth (n − 1)-dimensional varieties of lines in P verifying that all their lines meet a curve. This also gives a complete classification of (n− 1)-scrolls over a curve contained in G(1, n). Introduction. The geometry of the line, i.e. the study of the line as the main element, was a very popular subject at the end of last century and beginning...

On Linear Spaces of Skew-symmetric Matrices of Constant Rank

Linear sections of the Grassmannians G(1, n) of lines in P appear naturally in several different situations. In complex projective algebraic geometry, 3-dimensional linear sections of G(1, 4) appear in the classification of Fano threefolds, 2-dimensional linear sections of G(1, 5) define one of the smooth scrolls of P. Linear sections of dimension n − 1 of the Grassmannian of lines of P are cla...

Concurrent Constraints in the Fusion Calculus ( extended

We use the fusion calculus, a generalization and simpliication of the-calculus, to model concurrent constraint programming. In particular we encode three basic variants of the-calculus, which is a foundational calculus for the concurrent constraint programming language Oz. Using a new reduction-based semantics and weak barbed congruences for the fusion calculus we formally establish an operatio...

Isogonal congruences of circles are thus a generalization of normal congruences of circles, of normal congruences of lines, and of certain congruences of lines which naturally arise in connection with the parallel mapping of surfaces*. Isogonal