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.
arXiv:math.DG/0211159 (2002)
9 Pith papers cite this work. Polarity classification is still indexing.
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Riemannian manifolds with a closed parallel torsion 3-form are locally N × G (G semisimple), enabling simplified proofs and explicit classification of strong G2, Spin(7), and certain 8D HKT manifolds.
Proves rotational symmetry for nontrivial complete shrinking gradient Yamabe solitons under a scalar curvature lower bound with strict inequality somewhere.
Complete classification of nontrivial non-flat two- and three-dimensional complete gradient Yamabe solitons.
Local Ricci curvature and ν-entropy gap theorems for Ricci shrinkers depend only on dimension, generalizing prior global results and giving a local removable singularity criterion for Ricci flow.
Gradient Ricci shrinkers satisfy topological constraints including bounded Betti numbers and a Hodge theorem via weighted L2 cohomology.
Complete classification of nontrivial complete expanding gradient Yamabe solitons when scalar curvature exceeds or falls below the soliton constant.
Relative volume comparison theorem established under L^p bounds on Bakry-Émery Ricci curvature and potential gradient, applied to monotonicity in Kähler-Ricci flow.
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.
citing papers explorer
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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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On the rigidity of special and exceptional geometries with torsion a closed $3$-form
Riemannian manifolds with a closed parallel torsion 3-form are locally N × G (G semisimple), enabling simplified proofs and explicit classification of strong G2, Spin(7), and certain 8D HKT manifolds.
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Rotational symmetry of complete shrinking gradient Yamabe solitons
Proves rotational symmetry for nontrivial complete shrinking gradient Yamabe solitons under a scalar curvature lower bound with strict inequality somewhere.
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Classification of low-dimensional complete gradient Yamabe solitons
Complete classification of nontrivial non-flat two- and three-dimensional complete gradient Yamabe solitons.
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Rigidity and gap theorems for Ricci shrinkers
Local Ricci curvature and ν-entropy gap theorems for Ricci shrinkers depend only on dimension, generalizing prior global results and giving a local removable singularity criterion for Ricci flow.
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Topology of gradient Ricci shrinkers via weighted $L^2$ cohomology
Gradient Ricci shrinkers satisfy topological constraints including bounded Betti numbers and a Hodge theorem via weighted L2 cohomology.
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Triviality, Rotational Symmetry, and Classification of Complete Expanding Gradient Yamabe Solitons
Complete classification of nontrivial complete expanding gradient Yamabe solitons when scalar curvature exceeds or falls below the soliton constant.
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Weighted volume comparison and monotonicity for $L^p$-bound of Bakry-\'{E}mery Ricci curvature
Relative volume comparison theorem established under L^p bounds on Bakry-Émery Ricci curvature and potential gradient, applied to monotonicity in Kähler-Ricci flow.
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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.