Related papers: Webs and projective structures on a plane

A metric projective structure is a manifold equipped with the unparametrised geodesics of some pseudo-Riemannian metric. We make acomprehensive treatment of such structures in the case that there is a projective Weyl curvature nullity…

A pair of planes, both projective or both affine, of the same order and on the same pointset are orthogoval if each line of one plane intersects each line of the other plane in at most two points. In this paper we prove new constructions…

A projective structure on a compact Riemann surface X of genus g is given by an atlas with transition functions in PGL(2,C). Equivalently, a projective structure is given by a projective sl(2,C)-bundle over X equipped with a section s and a…

One of the well-known results in concurrency theory concerns the relationship between event structures and occurrence nets: an occurrence net can be associated with a prime event structure, and vice versa. More generally, the relationships…

For a torsionless connection on the tangent bundle of a manifold M the Weyl curvature W is the part of the curvature in kernel of the Ricci contraction. We give a coordinate free proof of Weyl's result that the Weyl curvature vanishes if…

We develop a dimension-independent theory of alignment in Lorentzian geometry, and apply it to the tensor classification problem for the Weyl and Ricci tensors. First, we show that the alignment condition is equivalent to the PND equation.…

An oriented link projection is the image of a generic immersion of oriented circles into the 2-sphere. The circle arrangement of a link projection is a disjoint union of unoriented circles on the 2-sphere obtained by orientation-incoherent…

It is considered a differentiable manifold equipped with a pseudo-Riemannian metric and an almost contact 3-struc\-ture so that an almost contact metric structure and two almost contact B-metric structures are generated. There are…

A class of nets in constructive (in A.A.Markov's sense) topological space for which the convergence is equivalent to convergence of all subsequences, is described. B.A.Kushner's theorem about coincidence of strong and weak constructive…

As true as it is that a bricklayer needs a plumb line and a T-square, so it is that a physicist using general relativity needs how to draw geodesics and use fields of congruent vector frames of reference. While the first part of the…

Webs are graphical objects that give a tangible, combinatorial way to compute and classify tensor invariants. Recently, [Gaetz, Pechenik, Pfannerer, Striker, Swanson 2023+] found a rotation-invariant web basis for $\mathrm{SL}_4$, as well…

Analogues of the classical affine-projective correspondence are developed in the context of statistical manifolds compatible with a radiant vector field. These utilize a formulation of Einstein equations for special statistical structures…

We explore the different geometric structures that can be constructed from the class of pairs of 2nd order PDE's that satisfy the condition of a vanishing generalized W\"{u}nschmann invariant. This condition arises naturally from the…

In this paper we prove that all manifolds with affine connection are globally projectively equivalent to some space with equiaffine connection (equiaffine manifold). These manifolds are characterised by a symmetric Ricci tensor.

We study the problem of classifying local projective structures in dimension two having non trivial Lie symmetries. In particular we obtain a classification of flat projective structures having positive dimensional Lie algebra of projective…

We study the sets of planes in an even dimensional real vector space $V$ which are simultaneously stabilised by a pair of complex structures on $V$. We completely describe these sets of planes for pairs of orthogonal complex structures.…

Every compact Riemann surface $X$ admits a natural projective structure $p_u$ as a consequence of the uniformization theorem. In this work we describe the construction of another natural projective structure on $X$, namely the Hodge…

We give a simple analytic criterion which characterizes linearizable 1-codimensional webs. Then we give an invariant geometrical interpretation of it, in term of projective connection. We explain then how our approach allows to study…

This paper completes the classification of nets of conics containing at least one double line in $\mathrm{PG}(2,q)$ for $q$ even. This classification contributes to the classification of partially symmetric tensors in $\mathbb{F}_q^3…

Solutions of an implicit ODE form a web. Already for cubic ODEs the 3-web of solutions has a nontrivial local invariant, namely the curvature form. Thus any local classification of implicit ODEs necessarily has functional moduli if no…