Solvable extensions of negative Ricci curvature of filiform Lie groups |
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| Authors: | Y Nikolayevsky |
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| Affiliation: | Department of Mathematics and Statistics, La Trobe University, Melbourne, Australia |
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| Abstract: | We give necessary and sufficient conditions of the existence of a left‐invariant metric of strictly negative Ricci curvature on a solvable Lie group the nilradical of whose Lie algebra  is a filiform Lie algebra  . It turns out that such a metric always exists, except for in the two cases, when  is one of the algebras of rank two,  or  , and  is a one‐dimensional extension of  , in which cases the conditions are given in terms of certain linear inequalities for the eigenvalues of the extension derivation. |
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| Keywords: | Solvable Lie algebra filiform Lie algebra nilradical negative Ricci curvature 53C30 22E25 |
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