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On integrability of generalized Veronese curves of distributions

Andriy Panasyuk
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Abstract

Given a 1-parameter family of 1-forms $\g(t)= \g_0+t\g_1+...+t^n\g_n$, consider the condition $d\g(t)\wedge\g(t)=0$ (of integrability for the annihilated by $\g(t)$ distribution $w(t)$). We prove that in order that this condition is satisfied for any $t$ it is sufficient that it is satisfied for $N=n+3$ different values of $t$ (the corresponding implication for $N=2n+1$ is obvious). In fact we give a stronger result dealing with distributions of higher codimension. This result is related to the so-called Veronese webs and can be applied in the theory of bihamiltonian structures.

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BibTeXRIS

Andriy Panasyuk. 2002-09-20. On integrability of generalized Veronese curves of distributions. https://doi.org/10.1016/s0034-4877(02)80059-3

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