Ricci-Flat Manifolds, Parallel Spinors and the Rosenberg Index

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• Main Author: Tony, Thomas
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/214094
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Ricci-Flat Manifolds, Parallel Spinors and the Rosenberg Index. Thomas Tony. SIGMA 21 (2025), 072, 7 pages

Every closed connected Riemannian spin manifold of non-zero Â-genus or non-zero Hitchin invariant with non-negative scalar curvature admits a parallel spinor, in particular is Ricci-flat. In this note, we generalize this result to closed connected spin manifolds of non-vanishing Rosenberg index. Thi...