MULTIPLICITY OF SOLUTIONS TO THE YAMABE PROBLEM ON COLLAPSING RIEMANNIAN SUBMERSIONS

Autor(es)

Bettiol, Renato G. ^[1] ; Piccione, Paolo ^[2]

Afiliação do(s) autor(es)

^[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 - USA

^[2] Univ Sao Paulo, Dept Matemat, BR-05508090 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: PACIFIC JOURNAL OF MATHEMATICS; v. 266, n. 1, p. 1-21, NOV 2013.
• Citações Web of Science: 14

Resumo

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)

• Processo FAPESP: 11/21362-2 - Ações de grupos, teoria de subvariedades, e análise global em geometria Riemanniana e pseudo-riemanniana
• Beneficiário: Paolo Piccione
• Modalidade de apoio: Auxílio à Pesquisa - Temático