Leafwise symplectic structures on Lawson’s foliation

The aim of this paper is to show that Lawson’s foliation on the $5$-sphere admits a smooth leafwise symplectic structure. The main part of the construction is to show that the Fermat type cubic surface admits an end-periodic symplectic structure. The results is paraphrased that the $5$-sphere admits a regular Poisson structure of symplectic dimension $4$.

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This research is partly supported by Grant-in-Aid for Scientific Research (B) 22340015.

Received 21 July 2015

Accepted 8 December 2017

Published 26 November 2018