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arXiv · 1601.06972

A numerical treatment to the problem of the quantity of Einstein metrics on flag manifolds

Lino Grama·Ricardo Miranda Martins
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Abstract

In this paper we employ numerical methods to study the Einstein equation \[ Ric(g)=λ\, g, \] where $Ric$ is the Ricci tensor and $λ$ is the Einstein constant, restricted to a class of full flag manifolds. These metrics describe the gravitational field of a vacuum with cosmological constant (vacuum is the case $λ=0$). In particular, we give estimates to the number of such metrics on the full flag manifolds $SU(n+1)/T^n$ for $n=4,5$, improving some classical estimatives. We also examine the isometric problem for these Einstein metrics. Our method can be applied for any fixed $n$.

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Lino Grama, Ricardo Miranda Martins. 2016-03-16. A numerical treatment to the problem of the quantity of Einstein metrics on flag manifolds. https://arxiv.org/abs/1601.06972

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