Abstract
On a closed connected oriented manifold M we study the space M-parallel to(M) of all Riemannian metrics which admit a non-zero parallel spinor on the universal covering. Such metrics are Ricci-flat, and all known Ricci-flat metrics are of this form. We show the following: The space M-parallel to(M) is a smooth submanifold of the space of all metrics and its premoduli space is a smooth ...
Abstract
On a closed connected oriented manifold M we study the space M-parallel to(M) of all Riemannian metrics which admit a non-zero parallel spinor on the universal covering. Such metrics are Ricci-flat, and all known Ricci-flat metrics are of this form. We show the following: The space M-parallel to(M) is a smooth submanifold of the space of all metrics and its premoduli space is a smooth finite-dimensional manifold. The holonomy group is locally constant on M-parallel to(M). If M is spin, then the dimension of the space of parallel spinors is a locally constant function on M-parallel to(M).
Altmetric