Ricci-Flat Manifolds, Parallel Spinors and the Rosenberg Index

Key Points

• Every closed connected riemannian spin manifold with non-zero A-genus or hitchin invariant has a parallel spinor, indicating the presence of special holonomy.
• Manifolds with non-negative scalar curvature, belonging to the ricci-flat category, also support parallel spinors, highlighting their geometric properties.
• We generalize the established criterion to closed connected spin manifolds with non-vanishing rosenberg index, expanding the understanding of spinors.
• This research suggests that ricci-flat spin manifolds of dimension two or higher with rosenberg index exhibit special holonomy, offering insights into their structure.