Calabi-Yau structures on cotangent bundles

Abstract

Starting with a orientable compact real-analytic Riemannian manifold $(L,g)$ with $\chi (L) = 0$, we show that a small neighborhood $\mathrm{Op}(L)$ of the zero section in the cotangent bundle $T*L$ carries a Calabi–Yau structure such that the zero section is an isometrically embedded special Lagrangian submanifold.