An example of special Lagrangian fibration (Q882947)

In this paper the author constructs an example which shows (using Calabi-Yau manifolds), how to build up of Harvey-Lawson's models on the total space of the line bundle \[ \pi :\pi _{1}^{\ast }T^{\ast }P_{1}\otimes \pi _{2}^{\ast }T^{\ast }P^{1}\rightarrow P_{1}\times P^{1}, \] a complete Ricci-flat Kähler metric and a smooth special Lagrangian fibration (using the method of Goldstein and Gross). This special Lagrangian fibration is smoothly built up of 4 Harvey-Lawson's models in 4 directions. The central fiber is homeomorphic to \( S^{1}\times S^{1}\times \mathbb R\).