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Holonomy rigidity for Ricci-flat metrics

Ammann, Bernd ; Kröncke, Klaus ; Weiss, Hartmut ; Witt, Frederik



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 ...

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