I am reading an article on Mirror Symmetry, where an example is given : the two (real) dimensional torus.
My question is a basic one : taking the symplectic form (if ones focuses on the symplectic aspect) to be the area form, the author says that Lagrangians (submanifolds closed by this form) are just lines.
Is this simply because lines are the zero area submanifolds? Why there aren't more than these?
Thank you.