Remark on a diameter bound for complete Riemannian manifolds with positive Bakry-Émery Ricci curvature

DOI10.1016/J.DIFGEO.2015.11.001zbMath1330.53051arXiv1504.05384OpenAlexW2288873622WikidataQ115355803 ScholiaQ115355803MaRDI QIDQ901072

Homare Tadano

Publication date: 23 December 2015

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.05384

zbMATH Keywords

index formRicci solitonBakry-Émery Ricci curvatureHitchin-Thorpe inequalityupper diameter bound

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (18)

Myers' type theorem with the Bakry-Émery Ricci tensor ⋮ A Myers-type compactness theorem by the use of Bakry-Emery Ricci tensor ⋮ Two compactness theorems on Finsler manifolds with positive weighted Ricci curvature ⋮ Diameter estimate for a class of compact generalized quasi-Einstein manifolds ⋮ Myers-type theorems via m-Bakry–Émery Ricci curvatures of quartic decays ⋮ Comparison geometry for integral radial Bakry-Émery Ricci tensor bounds ⋮ Some Ambrose- and Galloway-type theorems via Bakry-Émery and modified Ricci curvatures ⋮ Some Cheeger-Gromov-Taylor type compactness theorems via \(m\)-Bakry-Émery and \(m\)-modified Ricci curvatures ⋮ Myers' theorem for complete Riemannian hypersurfaces ⋮ Comparison geometry for integral Bakry-Émery Ricci tensor bounds ⋮ Remark on a lower diameter bound for compact shrinking Ricci solitons ⋮ Some compactness theorems via \(m\)-Bakry-Émery and \(m\)-modified Ricci curvatures with negative \(m\) ⋮ Sharp upper diameter bounds for compact shrinking Ricci solitons ⋮ Myers' type theorem for integral Bakry-Émery Ricci tensor bounds ⋮ Boju–Funar type theorems via m-Bakry–Émery and m-modified Ricci curvatures ⋮ \(m\)-Bakry-Émery Ricci curvatures, Riccati inequalities, and bounded diameters ⋮ Myers-type compactness theorem with the Bakry-Emery Ricci tensor ⋮ Extensions of Bonnet-Myers-type theorems with the Bakry-Emery Ricci curvature

Cites Work

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• Remarks on compact shrinking Ricci solitons of dimension four
• The Bakry-Emery Ricci tensor and its applications to some compactness theorems
• Strong uniqueness of the Ricci flow
• Comparison geometry for the Bakry-Emery Ricci tensor
• On the first eigenvalue of the Witten-Laplacian and the diameter of compact shrinking solitons
• Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds
• Recent Progress on Ricci Solitons
• DIAMETER BOUNDS AND HITCHIN-THORPE INEQUALITIES FOR COMPACT RICCI SOLITONS

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