A gap theorem for complete noncompact manifolds with nonnegative Ricci curvature. (English) Zbl 1011.53036
The paper concerns the gap phenomena on non-maximal volume growth manifolds. Using the Yamabe flow the authors prove that if the Ricci curvature of a complete non-compact locally conformally flat manifold is nonnegative, the scalar curvature is bounded and decays faster than quadratic at infinity, then the manifold is flat.
Reviewer: M.Hotloś (Wrocław)
MSC:
53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
53C20 | Global Riemannian geometry, including pinching |