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<p>We study the smallest positive eigenvalue <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda _1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>λ</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> of the Laplace–Beltrami operator associated with any compact strongly isotropy irreducible space. We provide an explicit expression for all simply connected cases. Furthermore, every strongly isotropy irreducible space is automatically an Einstein manifold, and we prove for each of them that <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(E&lt;\lambda _1\le 16E\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>E</mi> <mo>&lt;</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo>≤</mo> <mn>16</mn> <mi>E</mi> </mrow> </math></EquationSource> </InlineEquation>, where <i>E</i> denotes the corresponding Einstein constant.</p>

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First Laplace eigenvalue of strongly isotropy irreducible spaces

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • Emilio A. Lauret,
  • Fiorela Rossi Bertone,
  • Alejandro Tolcachier

摘要

We study the smallest positive eigenvalue \(\lambda _1\) λ 1 of the Laplace–Beltrami operator associated with any compact strongly isotropy irreducible space. We provide an explicit expression for all simply connected cases. Furthermore, every strongly isotropy irreducible space is automatically an Einstein manifold, and we prove for each of them that \(E<\lambda _1\le 16E\) E < λ 1 ≤ 16 E , where E denotes the corresponding Einstein constant.