On integrability of generalized Veronese curves of distributions

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.

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

References in corpus (2)

• Nonlinear wave equation, nonlinear Riemann problem, and the twistor transform of Veronese webs
• Veronese webs for bihamiltonian structures of higher corank

Cited by in corpus (5)

• On the local theory of Veronese webs
• Germs of integrable forms and varieties of minimal degree
• The Local Product Theorem for bihamiltonian structures
• Veronese curves and webs interpolation
• Differential Geometry of Veronese Webs