dc.contributor.author Knieper, Gerhard dc.contributor.author Parker, John R. dc.contributor.author Peyerimhoff, Norbert dc.date.accessioned 2019-05-08T09:28:59Z dc.date.available 2019-05-08T09:28:59Z dc.date.issued 2019-05-07 dc.identifier.uri http://publications.mfo.de/handle/mfo/1416 dc.description.abstract In this article we consider solvable hypersurfaces of the form $N \exp(\mathbb{R} H)$ with induced metrics in the symmetric space $M = SL(3,\mathbb{C})/SU(3)$, where $H$ a suitable unit length vector in the subgroup $A$ of the Iwasawa decomposition $SL(3,\mathbb{C}) = NAK$. Since $M$ is rank $2$, $A$ is $2$-dimensional and we can parametrize these hypersurfaces via an angle $\alpha \in [0,\pi/2]$ determining the direction of $H$. We show that one of the hypersurfaces (corresponding to $\alpha = 0$) is minimally embedded and isometric to the non-symmetric $7$-dimensional Damek-Ricci space. We also provide an explicit formula for the en_US Ricci curvature of these hypersurfaces and show that all hypersurfaces for $\alpha \in (0,\frac{\pi}{2}]$ 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. dc.language.iso en_US en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation Also published in: Differential Geometry and its Applications 69 (2020). DOI: 10.1016/j.difgeo.2020.101605 dc.relation.ispartofseries Oberwolfach Preprints;2019,11 dc.subject Damek-Ricci spaces en_US dc.subject Harmonic manifolds en_US dc.subject Minimal foliations en_US dc.title Minimal Codimension One Foliation of a Symmetric Space by Damek-Ricci Spaces en_US dc.type Preprint en_US dc.rights.license Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. de dc.rights.license This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. en dc.identifier.doi 10.14760/OWP-2019-11 local.scientificprogram Research in Pairs 2019 en_US local.series.id OWP-2019-11 en_US local.subject.msc 53 en_US dc.identifier.urn urn:nbn:de:101:1-2019051609353601566095 local.publishers-doi 10.1016/j.difgeo.2020.101605 dc.identifier.ppn 1665793872
﻿