Geometry and topology under positive/nonnegative sectional curvature
| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [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
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Geometriae Dedicata; v. 205, n. 1, p. 129-146, APR 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Research Projects - Thematic Grants |