Scholarlink

<p>We make classifications of gradient Ricci solitons (<i>M</i>,&#xa0;<i>g</i>,&#xa0;<i>f</i>) with harmonic Weyl curvature. As a local classification, we show that the associated Riemannian metric <i>g</i> is locally among the types (i)–(iv) in Theorem <InternalRef RefID="FPar1">1</InternalRef>. Compared with the previous four-dimensional study in [<CitationRef CitationID="CR25">25</CitationRef>], we have developed a novel method of <i>refined adapted frame fields</i> and overcome the main difficulty arising from a large number of Riemmannian connection components in dimension<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_1983_Article_IEq1.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\( \ge 5\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>≥</mo> <mn>5</mn> </mrow> </math></EquationSource> </InlineEquation>. Next we have obtained a classification of <i>complete</i> ones with harmonic Weyl curvature. For the proof, using the real analytic nature of <i>g</i> and <i>f</i>, we elaborate geometric arguments to fit together local regions.</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

Classification of Gradient Ricci Solitons with Harmonic Weyl Curvature

  • 期刊论文

  • 发表日期：

    2025年3月27日

查看全文
  • Jongsu Kim

摘要

We make classifications of gradient Ricci solitons (M, g, f) with harmonic Weyl curvature. As a local classification, we show that the associated Riemannian metric g is locally among the types (i)–(iv) in Theorem 1. Compared with the previous four-dimensional study in [25], we have developed a novel method of refined adapted frame fields and overcome the main difficulty arising from a large number of Riemmannian connection components in dimension \( \ge 5\) ≥ 5 . Next we have obtained a classification of complete ones with harmonic Weyl curvature. For the proof, using the real analytic nature of g and f, we elaborate geometric arguments to fit together local regions.