| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 - USA
[2] Univ Sao Paulo, Dept Matemat, BR-05508090 Sao Paulo - Brazil
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | PACIFIC JOURNAL OF MATHEMATICS; v. 266, n. 1, p. 1-21, NOV 2013. |
| Web of Science Citations: | 14 |
| Abstract | |
Let g(t) be a family of constant scalar curvature metrics on the total space of a Riemannian submersion obtained by shrinking the fibers of an original metric g, so that the submersion collapses as t -> 0 (that is, the total space converges to the base in the Gromov-Hausdorff sense). We prove that, under certain conditions, there are at least 3 unit volume constant scalar curvature metrics in the conformal class {[}g(t)] for infinitely many t accumulating at 0. This holds, for instance, for homogeneous metrics g(t) obtained via Cheeger deformation of homogeneous fibrations with fibers of positive scalar curvature. (AU) | |
| FAPESP's process: | 11/21362-2 - Group actions, submanifold theory and global analysis in Riemannian and pseudo-Riemannian geometry |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Research Projects - Thematic Grants |