Special Lagrangian manifolds obtained from complex Grassmannians (original) (raw)

This paper gives an example of special Lagrangian manifold obtained from a hypersurface of a complex Grassmannian with vanishing first Chern class. The obtained manifold is a 1-torus bundle over the two dimensional real projective space. Such manifolds are interesting for mirror symmetry theory. Other examples of the same type are provided at the end of this article. Introduction. In 1982, when F. Harvey and H. Lawson introduced Special Lagrangian manifolds in [7], their main interest was calibration problems. Now, these manifolds give another approach to mirror symmetry and string theory and become crucial in these fields. A conjecture due to Strominger, Yau and Zaslow in [9] explains mirror symmetry in a fairly