Analytic Foliation Divisorial Contraction on Sasakian Manifolds of Dimension Five

Abstract Let $$(M,\eta ,\xi ,\Phi ,g)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo>,</mml:mo> <mml:mi>η</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ξ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>Φ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>g</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> be a compact quasi-regular Sasakian 5 -manifold with finite cyclic quotient foliation singularities of type $$\frac{ 1}{r}(1,a).$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mi>r</mml:mi> </mml:mfrac> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>a</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> 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.