We show that, in contrast with the homogeneous case where a compact manifold always carries a non-negatively curved metric,the existence of such a metric on a cohomgeneity one manifold can be obstructed. We produce a large class of examples where this obstruction holds.
Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres / L. VERDIANI; GROVE K. ZILLER W. WILKING B. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - STAMPA. - V:(2006), pp. 1-12.
Non-negative curvature obstructions in cohomogeneity one and the Kervaire spheres
VERDIANI, LUIGI;
2006
Abstract
We show that, in contrast with the homogeneous case where a compact manifold always carries a non-negatively curved metric,the existence of such a metric on a cohomgeneity one manifold can be obstructed. We produce a large class of examples where this obstruction holds.
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