In this article we consider solvable hypersurfaces of the form N exp(RH) with induced metrics in the symmetric space M = SL(3, C)/SU(3), where Ha suitable unit length vector in the subgroup A of the Iwasawa decomposition SL(3, C) = NAK. Since Mis rank 2, A is 2-dimensional and we can parametrize these hypersurfaces via an angle alpha is an element of [-pi/2, 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 curvatures of these hypersurfaces and show that all hypersurfaces for alpha is an element of [-pi/2, 0) boolean AND (0, pi/2] admit planes of both negative and positive sectional curvature. Moreover, the symmetric space Madmits a minimal foliation with all leaves isometric to the non-symmetric 7-dimensional Damek-Ricci space. (C) 2020 Elsevier B.V. All rights reserved.
机构:
Univ Santiago de Compostela, Dept Geometry & Topol, Santiago De Compostela, SpainUniv Santiago de Compostela, Dept Geometry & Topol, Santiago De Compostela, Spain
Carlos Diaz-Ramos, Jose
Dominguez-Vazquez, Miguel
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Univ Santiago de Compostela, Dept Geometry & Topol, Santiago De Compostela, SpainUniv Santiago de Compostela, Dept Geometry & Topol, Santiago De Compostela, Spain
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Indian Stat Inst, Stat Math Unit, 203 BT Rd, Kolkata 700108, India
Indian Inst Technol, Dept Math, Mumbai 400076, Maharashtra, IndiaIndian Stat Inst, Stat Math Unit, 203 BT Rd, Kolkata 700108, India
机构:
Dipartimento Matemat, I-16146 Genoa, ItalyUniv Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy
Astengo, Francesca
Di Blasio, Bianca
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Univ Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, ItalyUniv Milano Bicocca, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy