Show simple item record

dc.contributor.authorKnieper, Gerhard
dc.contributor.authorParker, John R.
dc.contributor.authorPeyerimhoff, Norbert
dc.date.accessioned2019-05-08T09:28:59Z
dc.date.available2019-05-08T09:28:59Z
dc.date.issued2019-05-07
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1416
dc.description.abstractIn 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 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.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relationAlso published in: Differential Geometry and its Applications 69 (2020). DOI: 10.1016/j.difgeo.2020.101605
dc.relation.ispartofseriesOberwolfach Preprints;2019,11
dc.subjectDamek-Ricci spacesen_US
dc.subjectHarmonic manifoldsen_US
dc.subjectMinimal foliationsen_US
dc.titleMinimal Codimension One Foliation of a Symmetric Space by Damek-Ricci Spacesen_US
dc.typePreprinten_US
dc.rights.licenseDieses 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.licenseThis 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.doi10.14760/OWP-2019-11
local.scientificprogramResearch in Pairs 2019en_US
local.series.idOWP-2019-11en_US
local.subject.msc53en_US
dc.identifier.urnurn:nbn:de:101:1-2019051609353601566095
local.publishers-doi10.1016/j.difgeo.2020.101605
dc.identifier.ppn1665793872


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record