Some Ambrose- and Galloway-type theorems via Bakry-Émery and modified Ricci curvatures
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Publication:1692388
DOI10.2140/PJM.2018.294.213zbMath1380.53044OpenAlexW2783240426MaRDI QIDQ1692388
Publication date: 9 January 2018
Published in: Pacific Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2140/pjm.2018.294.213
Bakry-Émery Ricci curvaturesmooth metric measure spaceMyers-type theoremAmbrose-type theoremGalloway-type theoremmodified Ricci curvature
Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)
Related Items (6)
A note on compactness theorems for the Bakry-Émery Ricci tensor and generalized quasi-Einstein tensors ⋮ Some compactness theorems via \(m\)-Bakry-Émery and \(m\)-modified Ricci curvatures with negative \(m\) ⋮ \(m\)-Bakry-Émery Ricci curvatures, Riccati inequalities, and bounded diameters ⋮ Laplacian comparison theorem on Riemannian manifolds with modified \(m\)-Bakry-Emery Ricci lower bounds for \(m\leq1\) ⋮ Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature ⋮ Extensions of Bonnet-Myers-type theorems with the Bakry-Emery Ricci curvature
Cites Work
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- Remark on a diameter bound for complete Riemannian manifolds with positive Bakry-Émery Ricci curvature
- A generalization of Myers theorem and an application to relativistic cosmology
- Some geometric properties of the Bakry-Émery-Ricci tensor
- On the first eigenvalue of the Witten-Laplacian and the diameter of compact shrinking solitons
- A theorem of Ambrose for Bakry-Emery Ricci tensor
- Myer's theorem with density
- On Ricci curvature and geodesics
- Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds
- An upper diameter bound for compact Ricci solitons with application to the Hitchin–Thorpe inequality
- On a theorem of Ambrose
- Compactness Criteria for Riemannian Manifolds
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