2000/06/21 by Anand Dessai
Mathematics · #math.DG #math.GT #msc:53C25 #msc:55P35 #msc:53C27 #msc:53C29
published as Bull. London Math. Soc. 33, (2001), pp. 203-209 · revised version of preprint 45, SFB 478, Muenster; to appear in Bulletin of the LMS; 10 pages; no figures; MSC added
arxiv created 2000/06/21 · arxiv updated 2009/11/30
Let M be a simply-connected closed manifold of dimension ≥ 5 which does not admit a metric with positive scalar curvature. We give necessary conditions for M to admit a scalar-flat metric. These conditions involve the first Pontrjagin class and the cohomology ring of M. As a consequence any simply-connected scalar-flat manifold of dimension ≥ 5 with vanishing first Pontrjagin class admits a metric with positive scalar curvature. We also describe some relations between scalar-flat metrics, almost complex structures and the free loop space.