Geometry of isotypic Kronecker webs

• Autorzy: Wojciech Kryński
• Języki publikacji: EN

Abstrakty

EN

An isotypic Kronecker web is a family of corank m foliations $\{ \mathcal{F}_t \} _{t \in \mathbb{R}P^1 } $ such that the curve of annihilators t ↦ (T x F t)⊥ ∈ Grm(T x* M) is a rational normal curve in the Grassmannian Grm(T x*M) at any point x ∈ M. For m = 1 we get Veronese webs introduced by I. Gelfand and I. Zakharevich [Gelfand I.M., Zakharevich I., Webs, Veronese curves, and bi-Hamiltonian systems, J. Funct. Anal., 1991, 99(1), 150–178]. In the present paper, we consider the problem of local classification of isotypic Kronecker webs and for a given web we construct a canonical connection. We compute the curvature of the connection in the case of webs of equal rank and corank. We also show the correspondence between Kronecker webs and systems of ODEs for which certain sets of differential invariants vanish. The equations are given up to contact transformations preserving independent variable. As a particular case, with m = 1 we obtain the correspondence between Veronese webs and ODEs.

Słowa kluczowe

EN

Kronecker web; Veronese web; Ordinary differential equation

Kategorie tematyczne

• 34A26: Geometric methods in differential equations
• 53A60: Geometry of webs

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 5
• Strony: 1872-1888

Daty

wydano

2012-10-01

online

2012-07-24

Twórcy

autor

Wojciech Kryński

• Polish Academy of Sciences

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0081-z