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On One Class of Bol Three-Webs
In this paper, we consider infinitesimal properties of multidimensional median Bol threewebs with a covariantly constant curvature tensor (webs
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Note on generic singularities of planar flat 3-webs
We propose a definition of genericity for singular flat planar 3-webs formed by integral curves of implicit ODEs and give a classification of generic...
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Killing tensors with nonvanishing Haantjes torsion and integrable systems
The second-order integrable Killing tensor with simple eigenvalues and vanishing Haantjes torsion is the key ingredient in construction of Liouville...
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Equivalence of difference equations within the web theory
Elementary version of moving frame method is applied to the symmetries and equivalences of second-order difference equations. Close links to the web...
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On the Gronwall Conjecture
The Gronwall conjecture states that a planar 3-web which admits more than one distinct linearization is locally equivalent to an algebraic web. We...
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Geodesic Webs on a Two-Dimensional Manifold and Euler Equations
We prove that any planar 4-web defines a unique projective structure in the plane in such a way that the leaves of the web foliations are geodesics...
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On Implicit ODEs with Hexagonal Web of Solutions
Solutions of an implicit ODE form a web. Already for a cubic ODE the 3-web of solutions has a nontrivial local invariant, namely the curvature form....
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On Grassmannizable Group 3-Webs
The authors prove that the Lie group G generating a Grassmannizable group 3-web GGW is the group of parameters of the group of similarity...
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On the Blaschke conjecture for 3-webs
We find relative differential invariants of orders eight and nine for a planar nonparallelizable 3-web such that their vanishing is necessary and...
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Abelian functional equations, planar web geometry and polylogarithms
We study some abelian functional equations
(Afe) . They are equations in the F i ’s of the form F 1 ( U 1 ) + ... + F N ( U N ) = 0 where the U ... -
Linearizability of d-webs, d ≥ 4, on two-dimensional manifolds
We find d − 2 relative differential invariants for a d -web, d ≥ 4, on a two-dimensional manifold and prove that their vanishing is necessary and...
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Correction to: On Webs of Maximum Rank (Geom. Dedicata 31 (1989), 19–35)
We correct an error in Example (3.4) in Geom. Dedicata 31 (1989), 19–35.
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4-Webs in the Plane and Their Linearizability
We investigate the linearizability problem for different classes of 4-webs in the plane. In particular, we apply the linearizability conditions,...
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Formes différentielles abéliennes, bornes de Castelnuovo et géométrie des tissus
A $d$-web ${\Cal W}(d)$ is given by $d$ complex analytic foliations of codimension $n$ in $({\sumbbb C}^N,0)$ such that the leaves are in general...
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Webs with rotation and reflection properties and their relations with certain loops
In a web one can define in a natural way reflections in generators and a kind of rotations in points. The structure of the webs and the corresponding...
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Proportional nets in Weyl spaces
α-proportional and proportional nets in n -dimensional Weyl space W n and Riemannian space V n are introduced. The fundamental forms of the spaces W n ...
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Webs related to K-loops and reflection structures
We give a characterization of webs (
P ,g 1 ,g 2 ,g ) which are related to A 1 -loops, weak K -loops, K -loops and reflection structures. We also obtain a...