We consider an exotic contact form $\alpha$ on $S^3$ and we establish explicitly the existence of a non singular vector field $v$ in $ker(\alpha)$ such that the non-singular one-differential form $\beta(\cdot):=d\alpha(v,\cdot)$ is a contact form on $S^3$ with the same orientation than $\alpha$. In particular this means that a Legendre transform can be completed.
Vittorio Martino (2011). A Legendre transform on an exotic S^3. ADVANCED NONLINEAR STUDIES, 11, 145-156.
A Legendre transform on an exotic S^3
MARTINO, VITTORIO
2011
Abstract
We consider an exotic contact form $\alpha$ on $S^3$ and we establish explicitly the existence of a non singular vector field $v$ in $ker(\alpha)$ such that the non-singular one-differential form $\beta(\cdot):=d\alpha(v,\cdot)$ is a contact form on $S^3$ with the same orientation than $\alpha$. In particular this means that a Legendre transform can be completed.File in questo prodotto:
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