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

Knieper, Gerhard and Parker, John R. and Peyerimhoff, Norbert (2020) 'Minimal codimension one foliation of a symmetric space by Damek-Ricci spaces.', Differential geometry and its applications., 69 . p. 101605.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1016/j.difgeo.2020.101605
Publisher statement:© 2020 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Date accepted:28 January 2020
Date deposited:21 February 2020
Date of first online publication:07 February 2020
Date first made open access:07 February 2021

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