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arXiv · 1912.12686

Diagonalizing the Ricci Tensor

Anusha M. Krishnan
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Abstract

We show that a basis of a semisimple Lie algebra of compact type, for which any diagonal left-invariant metric has a diagonal Ricci tensor, is characterized by the Lie algebraic condition of being "nice". Namely, the bracket of any two basis elements is a multiple of another basis element. This extends the work of Lauret and Will on nilpotent Lie algebras. The result follows from a more general characterization for diagonalizing the Ricci tensor for homogeneous spaces. Finally, we also study the Ricci flow behavior of diagonal metrics on cohomogeneity one manifolds.

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Anusha M. Krishnan. 2019-12-29. Diagonalizing the Ricci Tensor. https://arxiv.org/abs/1912.12686

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