Scholarlink

<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((M, g, \omega , f, \lambda )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mi>g</mi> <mo>,</mo> <mi>ω</mi> <mo>,</mo> <mi>f</mi> <mo>,</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> be a Kähler gradient Ricci soliton in real dimension four. The first theorem states that it is an integrable Hamiltonian system in a classical sense. Furthermore, either it is of cohomogeneity one or the integrals of motion are given by the potential function <i>f</i> and the scalar curvature <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\mathrm S}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">S</mi> </math></EquationSource> </InlineEquation>. The second theorem states that if the system is non-degenerate and <i>f</i> is proper, then there is an effective, completely integrable Hamiltonian <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {T}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">T</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>- action.</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

Kähler Soliton Surfaces Are Generically Toric

  • 期刊论文

  • 发表日期：

    2025年9月8日

查看全文
  • Hung Tran

摘要

Let \((M, g, \omega , f, \lambda )\) ( M , g , ω , f , λ ) be a Kähler gradient Ricci soliton in real dimension four. The first theorem states that it is an integrable Hamiltonian system in a classical sense. Furthermore, either it is of cohomogeneity one or the integrals of motion are given by the potential function f and the scalar curvature \({\mathrm S}\) S . The second theorem states that if the system is non-degenerate and f is proper, then there is an effective, completely integrable Hamiltonian \(\mathbb {T}^2\) T 2 - action.