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<p>We study the splitting of Ricci shrinkers via eigenvalues. In our previous work Li-Zhang-Zhang (<i>J. Funct. Anal.</i> Vol. 290, 111386), we showed that on a Ricci shrinker, the eigenvalues close to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\frac{1}{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></EquationSource> </InlineEquation> implies the shrinker is almost splitting. In this paper, we obtain the converse, i.e., almost splitting implies the eigenvalues close to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\frac{1}{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </math></EquationSource> </InlineEquation>. This completes the characterization of almost splitting of Ricci shrinkers in terms of eigenvalue conditions.</p>

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Characterizing the Splitting of Ricci Shrinkers Via Eigenvalues

  • 期刊论文

  • 发表日期：

    2026年4月10日

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  • Huaiyu Zhang

摘要

We study the splitting of Ricci shrinkers via eigenvalues. In our previous work Li-Zhang-Zhang (J. Funct. Anal. Vol. 290, 111386), we showed that on a Ricci shrinker, the eigenvalues close to \(\frac{1}{2}\) 1 2 implies the shrinker is almost splitting. In this paper, we obtain the converse, i.e., almost splitting implies the eigenvalues close to \(\frac{1}{2}\) 1 2 . This completes the characterization of almost splitting of Ricci shrinkers in terms of eigenvalue conditions.