Einstein solvmanifolds attached to two-step nilradicals
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A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous Einstein space) is almost completely determined by the nilradical of its Lie algebra. A nilpotent Lie algebra which can serve as the nilradical of an Einstein metric solvable Lie algebra is called an Einstein nilradical. We give a classification of two-step nilpotent Einstein nilradicals with two-dimensional center. Informally, the defining matrix pencil must have no nilpotent blocks in the canonical form and no elementary divisors of a very high multiplicity. We also show that the dual to a two-step Einstein nilradical is not in general an Einstein nilradical.
KeywordsEinstein solvmanifold Einstein nilradical Two-step nilpotent Lie algebra
Mathematics Subject Classification (2000)53C30 53C25
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- 7.Eberlein P.: Geometry of 2-step nilpotent Lie groups. Modern Dynamical Systems, pp. 67–101. Cambridge University Press, Cambridge (2004)Google Scholar
- 8.Eberlein, P.: Riemannian 2-step nilmanifolds with prescribed Ricci tensor. Geometric and Probabilistic Structures in Dynamics. Contemporary Mathematics, vol. 469, pp. 167–195. American Mathematical Soceity, Providence (2008)Google Scholar
- 10.Gantmacher F.R.: The Theory of Matrices. vol. 1, 2. Chelsea Publishing Co., New York (1959)Google Scholar
- 14.Jablonski, M.: Real Geometric Invariant Theory and Ricci soliton metrics on two-step nilmanifolds. Thesis (2008)Google Scholar
- 19.Lauret J.: Einstein solvmanifolds and nilsolitons. New developments in Lie theory and geometry Contemporary Mathematics, vol. 491, pp. 1–35. American Mathematical Soceity, Providence (2009)Google Scholar
- 21.Nikolayevsky, Y.: Nilradicals of Einstein solvmanifolds. arXiv: math.DG/0612117 (Preprint, 2006)Google Scholar