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Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces

Knieper, Gerhard; Parker, John R; Peyerimhoff, Norbert

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Authors

Gerhard Knieper



Abstract

In this article we consider solvable hypersurfaces of the form with induced metrics in the symmetric space , where H a suitable unit length vector in the subgroup A of the Iwasawa decomposition . Since M is rank 2, A is 2-dimensional and we can parametrize these hypersurfaces via an angle determining the direction of H. We show that one of the hypersurfaces (corresponding to ) is minimally embedded and isometric to the non-symmetric 7-dimensional Damek-Ricci space. We also provide an explicit formula for the Ricci curvatures of these hypersurfaces and show that all hypersurfaces for admit planes of both negative and positive sectional curvature. Moreover, the symmetric space M admits a minimal foliation with all leaves isometric to the non-symmetric 7-dimensional Damek-Ricci space.

Citation

Knieper, G., Parker, J. R., & Peyerimhoff, N. (2020). Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces. Differential Geometry and its Applications, 69, Article 101605. https://doi.org/10.1016/j.difgeo.2020.101605

Journal Article Type Article
Acceptance Date Jan 28, 2020
Online Publication Date Feb 7, 2020
Publication Date Apr 30, 2020
Deposit Date Jan 28, 2020
Publicly Available Date Feb 7, 2021
Journal Differential Geometry and its Applications
Print ISSN 0926-2245
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 69
Article Number 101605
DOI https://doi.org/10.1016/j.difgeo.2020.101605

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