Acta Mathematica

, Volume 200, Issue 1, pp 1–13

Classification of manifolds with weakly 1/4-pinched curvatures

Article

DOI: 10.1007/s11511-008-0022-7

Cite this article as:
Brendle, S. & Schoen, R.M. Acta Math (2008) 200: 1. doi:10.1007/s11511-008-0022-7

Abstract

We show that a compact Riemannian manifold with weakly pointwise 1/4-pinched sectional curvatures is either locally symmetric or diffeomorphic to a space form. More generally, we classify all compact, locally irreducible Riemannian manifolds M with the property that M × R2 has non-negative isotropic curvature.

Copyright information

© Institut Mittag-Leffler 2008

Authors and Affiliations

  1. 1.Department of MathematicsStanford UniversityStanfordUSA