Parabolic subgroups of semisimple Lie groups and Einstein solvmanifolds

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dc.creatorTamaru, Hiroshi
dc.date2007-11-07
dc.date.accessioned2026-07-07T08:41:18Z
dc.date.available2026-07-07T08:41:18Z
dc.descriptionIn this paper, we study the solvmanifolds constructed from any parabolic subalgebras of any semisimple Lie algebras. These solvmanifolds are naturally homogeneous submanifolds of symmetric spaces of noncompact type. We show that the Ricci curvatures of our solvmanifolds coincide with the restrictions of the Ricci curvatures of the ambient symmetric spaces. Consequently, all of our solvmanifolds are Einstein, which provide a large number of new examples of noncompact homogeneous Einstein manifolds. We also show that our solvmanifolds are minimal, but not totally geodesic submanifolds of symmetric spaces.
dc.description16pages
dc.identifierhttps://arxiv.org/abs/0711.1022
dc.identifierhttp://arxiv.org/abs/0711.1022
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141638
dc.subjectDifferential Geometry
dc.subject53C30; 22E25
dc.titleParabolic subgroups of semisimple Lie groups and Einstein solvmanifolds
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