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<p>In this work, we will establish new classification results concerning <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10455_2025_9995_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda _1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>λ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-extremality for partial flag manifolds using a sufficient and necessary condition, in terms of Lie theoretic data, for a Kähler–Einstein metric over a generalized flag manifold to be a critical point for the functional that assigns for each Riemannian invariant Kähler metric its first positive eigenvalue of the associated Laplacian..</p>

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Riemannian \(\lambda _1\)-extremal metrics on generalized flag manifolds

  • 期刊论文

  • 发表日期：

    2025年5月28日

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  • Kennerson N. S. Lima

摘要

In this work, we will establish new classification results concerning \(\lambda _1\) λ 1 -extremality for partial flag manifolds using a sufficient and necessary condition, in terms of Lie theoretic data, for a Kähler–Einstein metric over a generalized flag manifold to be a critical point for the functional that assigns for each Riemannian invariant Kähler metric its first positive eigenvalue of the associated Laplacian..