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<p>Let <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((M,\eta ,\xi ,\Phi ,g)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mi>η</mi> <mo>,</mo> <mi>ξ</mi> <mo>,</mo> <mi mathvariant="normal">Φ</mi> <mo>,</mo> <mi>g</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> be a compact quasi-regular Sasakian 5 -manifold with finite cyclic quotient foliation singularities of type <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\frac{ 1}{r}(1,a).\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mrow> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> First, we derive the foliation minimal model program by applying the resolution of cyclic quotient foliation singularities. Secondly, based on the study of local model of resolution of foliation singularities, we prove the foliation canonical surgical contraction or the foliation external ray contraction under the Sasaki-Ricci flow. As a consequence, we prove a Sasaki analogue of analytic minimal model program with the Kähler-Ricci flow due to Song-Tian and Song-Weinkove.</p>

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Analytic Foliation Divisorial Contraction on Sasakian Manifolds of Dimension Five

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月29日

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  • Der-Chen Chang,
  • Shu-Cheng Chang,
  • Chien Lin,
  • Chin-Tung Wu

摘要

Let \((M,\eta ,\xi ,\Phi ,g)\) ( M , η , ξ , Φ , g ) be a compact quasi-regular Sasakian 5 -manifold with finite cyclic quotient foliation singularities of type \(\frac{ 1}{r}(1,a).\) 1 r ( 1 , a ) . First, we derive the foliation minimal model program by applying the resolution of cyclic quotient foliation singularities. Secondly, based on the study of local model of resolution of foliation singularities, we prove the foliation canonical surgical contraction or the foliation external ray contraction under the Sasaki-Ricci flow. As a consequence, we prove a Sasaki analogue of analytic minimal model program with the Kähler-Ricci flow due to Song-Tian and Song-Weinkove.