Diagonalizing the Ricci Tensor
| Autor: | Krishnan, Anusha M. |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | J. Geom. Anal. 31 (2021), no. 6, 5638-5658 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: LaTeX2e, 17 pages, final version |
| Databáze: | arXiv |
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