Negative Ricci curvature on some non-solvable Lie groups II

Cynthia E. Will

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arXiv · 1710.07714

Negative Ricci curvature on some non-solvable Lie groups II

Cynthia E. Will

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Abstract

We construct many examples of Lie groups with compact Levi factor admitting a left-invariant metric with negative Ricci curvature. We start with a Lie algebra with Levi factor su(n) or so(n) acting on an abelian nilradical via the representation on the space of homogeneous polynomials. In the case of su(2) we obtain a more general construction where the nilradical can be any nilpotent Lie algebra. We also prove a general result in the case when the Levi factor is a semisimple Lie algebra of non-compact type.

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Cynthia E. Will. 2017-10-20. Negative Ricci curvature on some non-solvable Lie groups II. https://arxiv.org/abs/1710.07714

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