Hypersurfaces of space forms carrying a totally geodesic foliation

Autor(es)

Dajczer, Marcos ^[1] ; Tojeiro, Ruy ^[2]

Afiliação do(s) autor(es)

^[1] IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro - Brazil

^[2] Univ Sao Paulo, Ave Trabalhador Sao Carlense 400, BR-13560970 Sao Carlos - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Geometriae Dedicata; v. 205, n. 1, p. 129-146, APR 2020.
• Citações Web of Science: 0

Resumo

In this paper we give a complete local parametric classification of the hypersurfaces with dimension at least three of a space form that carry a totally geodesic foliation of codimension one. A classification under the assumption that the leaves of the foliation are complete was already given in Dajczer et al. (Geometriae Dedicata 176:215-224, 2015) for Euclidean hypersurfaces. We prove that there exists exactly one further class of local examples in Euclidean space, all of which have rank two. We also extend the classification under the global assumption of completeness of the leaves for hypersurfaces of the sphere and show that there exist plenty of examples in hyperbolic space. (AU)

• Processo FAPESP: 16/23746-6 - Técnicas algébricas, topológicas e analíticas em geometria diferencial e análise geométrica
• Beneficiário: Paolo Piccione
• Linha de fomento: Auxílio à Pesquisa - Temático