ON COMPLETE METRICS OF NONNEGATIVE CURVATURE ON 2-PLANE BUNDLES

Authors
YANG DG
Citation
Dg. Yang, ON COMPLETE METRICS OF NONNEGATIVE CURVATURE ON 2-PLANE BUNDLES, Pacific journal of mathematics, 171(2), 1995, pp. 569-583
Citations number
7
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Pacific journal of mathematics → ACNP
ISSN journal
00308730
Volume
171
Issue
2
Year of publication
1995
Pages
569 - 583
Database
ISI
SICI code
0030-8730(1995)171:2<569:OCMONC>2.0.ZU;2-8
Abstract
This paper is an attempt to understand the 2-plane bundle case for the converse of the soul theorem due to J. Cheeger and D Gromoll. It is s hown that there is a class of 2-plane bundles over certain S-2-bundles that carry complete metrics of nonnegative sectional curvature. In pa rticular, every 2-plane bundle and every S-1-bundle over the connected sum CPn#<(CP)over bar>(n) of CPn with a negative CPn carries a 2-para meter family of complete metrics with nonnegative sectional curvature.