2002/10/10 by Kristopher Tapp, Tapp, Kristopher
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · #53C20 #Advanced Differential Geometry Research #Connective tissue disorders research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Ophthalmology and Eye Disorders
paper · pdf · doi:10.48550/arxiv.math/0210160
openalex publication_date 2002/10/10 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
This paper addresses Cheeger and Gromoll's question of which vector bundles\nadmit a complete metric of nonnegative curvature, and relates their question to\nthe issue of which sphere bundles admit a metric of positive curvature. We show\nthat any vector bundle which admits a metric of nonnegative curvature must\nadmit a connection, a tensor, and a metric on the base space which together\nsatisfy a certain differential inequality. On the other hand, a slight\nsharpening of this condition is sufficient for the associated sphere bundle to\nadmit a metric of positive curvature. Our results sharpen and generalize\nWalschap and Strake's conditions under which a vector bundle admits a\nconnection metric of nonnegative curvature.\n