The paper confirms the Hamilton-Tian conjecture for Sasaki-Ricci flow on compact transverse Fano quasi-regular Sasakian 5-manifolds with klt singularities, derives soliton compactness, and extends the result to general transverse Fano Sasakian 5-manifolds via the second Sasakian structure theorem.
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Establishes transverse rigidity criteria for shrinking Sasaki-Ricci solitons and classifies low-dimensional constant-scalar-curvature examples as Sasaki-Einstein plus harmonic-Weyl cases as spherical quotients.
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On the Hamilton-Tian Conjecture in a compact transverse Fano Sasakian $5$-manifold
The paper confirms the Hamilton-Tian conjecture for Sasaki-Ricci flow on compact transverse Fano quasi-regular Sasakian 5-manifolds with klt singularities, derives soliton compactness, and extends the result to general transverse Fano Sasakian 5-manifolds via the second Sasakian structure theorem.
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Transverse Rigidity of Shrinking Sasaki-Ricci Solitons
Establishes transverse rigidity criteria for shrinking Sasaki-Ricci solitons and classifies low-dimensional constant-scalar-curvature examples as Sasaki-Einstein plus harmonic-Weyl cases as spherical quotients.