Abstract
We obtain new examples of non-symmetric Einstein solvmanifolds by combining two techniques. In Tamaru (Parabolic subgroups of semisimple Lie groups and einstein solvmanifolds. Math Ann 351(1):51–66, 2011) constructs new attached solvmanifolds, which are submanifolds of the solvmanifolds correspond to noncompact symmetric spaces, endowed with a natural metric. Extending this construction, we apply it to associated solvmanifolds, described in (Ann Global Anal Geom 19(1):75–101, 2001), obtained by modifying the algebraic structure of the solvable Lie algebras corresponding to noncompact symmetric spaces. Our new examples are Einstein solvmanifolds with nilradicals of high nilpotency, which are geometrically distinct from noncompact symmetric spaces and their submanifolds.
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Kerr, M.M. New examples of non-symmetric Einstein solvmanifolds of negative Ricci curvature. Ann Glob Anal Geom 46, 281–291 (2014). https://doi.org/10.1007/s10455-014-9423-3
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DOI: https://doi.org/10.1007/s10455-014-9423-3