Negative Ricci curvature on some non-solvable Lie groups |
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Authors: | Cynthia E Will |
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Institution: | 1.Universidad Nacional de Córdoba, FaMAF and CIEM,Córdoba,Argentina |
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Abstract: | We show that for any non-trivial representation \((V, \pi )\) of \(\mathfrak {u}(2)\) with the center acting as multiples of the identity, the semidirect product \(\mathfrak {u}(2) \ltimes _\pi V\) admits a metric with negative Ricci curvature that can be explicitly obtained. It is proved that \(\mathfrak {u}(2) \ltimes _\pi V\) degenerates to a solvable Lie algebra that admits a metric with negative Ricci curvature. An n-dimensional Lie group with compact Levi factor \(\mathrm {SU}(2)\) admitting a left invariant metric with negative Ricci is therefore obtained for any \(n \ge 7\). |
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