Rigidity for Nonnegatively Curved Metrics on S²xR³

2002/10/10 by Kristopher Tapp, Tapp, Kristopher
Mathematics · #53C20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C20

paper · pdf · doi:10.48550/arxiv.math/0210157

arxiv created 2002/10/10 · arxiv updated 2009/11/30

Abstract

We address the question: how large is the family of complete metrics with nonnegative sectional curvature on S²xR³? We classify the connection metrics, and give several examples of non-connection metrics. We provide evidence that the family is small by proving some rigidity results for metrics more general than connection metrics.

Related

• Metrics with Nonnegative Curvature on S²xR⁴
• Rigidity of non-negatively curved metrics on open five-dimensional manifolds
• Nonnegatively curved metrics on S²xR²
• Extremal metrics involving scalar curvature
• Topological and geometric rigidity of nonnegatively curved submanifolds