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• W3100174916 endingPage "764" @default.
• W3100174916 startingPage "735" @default.
• W3100174916 abstract "In this work we investigate solvable and nilpotent Lie groups with special metrics. The metrics of interest are left-invariant Einstein and algebraic Ricci soliton metrics. Our main result shows that the existence of a such a metric is intrinsic to the underlying Lie algebra. More precisely, we show how one may determine the existence of such a metric by analyzing algebraic properties of the Lie algebra in question and infinitesimal deformations of any initial metric. Our second main result concerns the isometry groups of such distinguished metrics. Among the completely solvable unimodular Lie groups (this includes nilpotent groups), if the Lie group admits such a metric, we show that the isometry group of this special metric is maximal among all isometry groups of left-invariant metrics. We finish with a similar result for locally left-invariant metrics on compact nilmanifolds." @default.
• W3100174916 created "2020-11-23" @default.
• W3100174916 creator A5087675146 @default.
• W3100174916 date "2011-05-14" @default.
• W3100174916 modified "2023-10-11" @default.
• W3100174916 title "Concerning the existence of Einstein and Ricci soliton metrics on solvable Lie groups" @default.
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• W3100174916 doi "https://doi.org/10.2140/gt.2011.15.735" @default.
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