We investigate integrable second-order equations of the form F(u_xx,u_xy,u_yy,u_xt,u_yt,
u_tt)=0, which typically arise as the Hirota-type relations for various (2+ 1)-dimensional …

We show that classical Wilczynski-Se-ashi invariants of linear systems of ordinary differential
equations are generalized in a natural way to contact invariants of non-linear ODEs. We …

We discuss the twistor correspondence between path geometries in three dimensions with
vanishing Wilczynski invariants and anti-self-dual conformal structures of signature (2, 2) …

This article is concerned with causal structures, which are defined as a field of tangentially
non-degenerate projective hypersurfaces in the projectivized tangent bundle of a manifold …

We study five dimensional geometries associated with the 5-dimensional irreducible
representation of GL (2, R). These are special Weyl geometries in signature (3, 2) having the …

Let Gr (d, n) be the Grassmannian of d‐dimensional linear subspaces of an n‐dimensional
vector space V n. A submanifold X⊂ Gr (d, n) gives rise to a differential system Σ (X) that …

The fundamental invariants for vector ODEs of order $\ge 3$ considered up to point
transformations consist of generalized Wilczynski invariants and C-class invariants. An ODE …

Geometric realizations, curvature decompositions, and Weyl manifolds - ScienceDirect Skip
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Paraconformal or GL (2, ℝ) geometry on an n-dimensional manifold M is defined by a field of
rational normal curves of degree n–1 in the projectivised cotangent bundle ℙT* M. Such …

We study dynamic pairs (X, V) where X is a vector field on a smooth manifold M and V⊂ TM
is a vector distribution, both satisfying certain regularity conditions. We construct basic …