Mathematics > Differential Geometry
[Submitted on 14 Nov 2024]
Title:Einstein metrics on the full flag $F(n)$
View PDF HTML (experimental)Abstract:Let $ M = G/K $ be a full flag manifold. In this work, we investigate the $ G$-stability of Einstein metrics on $M$ and analyze their stability types, including coindices, for several cases. We specifically focus on $F(n) = \mathrm{SU}(n)/T$, emphasizing $n = 5$, where we identify four new Einstein metrics in addition to known ones. Stability data, including coindex and Hessian spectrum, confirms that these metrics on $F(5)$ are pairwise non-homothetic, providing new insights into the finiteness conjecture.
Submission history
From: Mikhail Eduardo Rios Guzman [view email][v1] Thu, 14 Nov 2024 22:53:10 UTC (20 KB)
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