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The existence of soliton metrics for nilpotent Lie groups, arXiv:0809.5068v1. 27 [Perb] Grisha Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv:mathDG/0211159. , Finite extinction time for the solutions to the Ricci f

By Tracy L. Payne


Abstract. We show that a left-invariant metric g on a nilpotent Lie group N is a soliton metric if and only if a matrix U and vector v associated the manifold (N, g) satisfy the matrix equation Uv = [1], where [1] is a vector with every entry a one. We associate a generalized Cartan matrix to the matrix U and use the theory of Kac-Moody algebras to analyze the solution spaces for such linear systems. We use these methods to find infinitely many new examples of nilmanifolds with soliton metrics. We give a sufficient condition for a sum of soliton metric nilpotent Lie algebra structures to be soliton, and we use this criterion to show that a soliton metric exists on every naturally graded filiform metric Lie algebra. 1

Year: 2013
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