Scholarlink

<p>Volume comparison theorem is a type of fundamental results in Riemannian geometry. In this article, we extend the volume comparison to the comparison of total <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\sigma _l\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mi>l</mi> </msub> </math></EquationSource> </InlineEquation>-curvature with respect to <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\sigma _k\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation>-curvature. In particular, we prove the comparison holds for metrics close to strictly stable positive Einstein metric when <i>k</i> and <i>l</i> satisfy certain assumptions. As for negative Einstein metrics, we prove a similar comparison result provided certain assumptions on sectional curvature holds for the manifold.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Comparison of Total \(\sigma _k\)-Curvature

  • 期刊论文

  • 发表日期：

    2026年2月16日

查看全文
  • Jiaqi Chen,
  • Yufei Shan,
  • Yinghui Ye

摘要

Volume comparison theorem is a type of fundamental results in Riemannian geometry. In this article, we extend the volume comparison to the comparison of total \(\sigma _l\) σ l -curvature with respect to \(\sigma _k\) σ k -curvature. In particular, we prove the comparison holds for metrics close to strictly stable positive Einstein metric when k and l satisfy certain assumptions. As for negative Einstein metrics, we prove a similar comparison result provided certain assumptions on sectional curvature holds for the manifold.