On integrability of generalized Veronese curves of distributions

Details On integrability of generalized Veronese curves of distributions On integrability of generalized Veronese curves of distributions

2002-09-20

arxiv.org/abs/math/0209261v1

Mathematics

Differential Geometry

7p., to appear in "Reports on Mathematical Physics"

Scientific paper

10.1016/S0034-4877(02)80059-3

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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