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- Title
Diameter estimates under integral radial m-Bakry–Émery Ricci curvature bounds.
- Authors
Tadano, Homare
- Abstract
By using some line integrals in terms of the radial m -Bakry–Émery and radial m -modified Bakry–Émery Ricci curvatures, we give various compactness criteria for complete Riemannian manifolds when m is a positive constant, a negative constant, or infinity. Our results not only guarantee the compactness of complete Riemannian manifolds allowing the presence of negative amounts of the radial m -Bakry–Émery and radial m -modified Bakry–Émery Ricci curvatures, but also give new Myers-type theorems via m -Bakry–Émery and m -modified Bakry–Émery Ricci curvatures even the line integrals are reduced to pointwise positive lower bounds on the m -Bakry–Émery and m -modified Bakry–Émery Ricci curvatures. The key ingredients in proving our results are Riccati inequalities obtained from Bochner–Weitzenböck formulas via m -Bakry–Émery and m -modified Bakry–Émery Ricci curvatures.
- Subjects
CURVATURE; LINE integrals; RIEMANNIAN manifolds; INTEGRALS; DIAMETER
- Publication
International Journal of Mathematics, 2024, Vol 35, Issue 8, p1
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X23500933