A special Lagrangian fibration in the Taub-NUT space

Abstract

In this paper we construct explicitly a special Lagrangian fibration in the Taub-NUT space. The Taub-NUT space is a complex 2-fold with a Ricci-flat metric and it is well known to physicists. For this space, we find S¹-invariant special Lagrangian submanifolds by using moment map techniques and show that a family of special Lagrangian submanifolds give a fibration of the Taub-NUT space. We also study a topology of special Lagrangian fibers using explicit description of special Lagrangians.