Details

Autor(en) / Beteiligte

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

Titel

Holonomy rigidity for Ricci-flat metrics

Ist Teil von

• Mathematische Zeitschrift, 2019-02, Vol.291 (1-2), p.303-311

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2019

Link zum Volltext

Quelle

SpringerLink (Online service)

Beschreibungen/Notizen

• On a closed connected oriented manifold M we study the space M ‖ ( 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 ‖ ( 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 ‖ ( M ) . If M is spin, then the dimension of the space of parallel spinors is a locally constant function on  M ‖ ( M ) .