Cheeger-Gromoll splitting theorem for the Bakry-Emery Ricci tensor

DOI10.1007/s00013-021-01658-1OpenAlexW3198422423MaRDI QIDQ2052378

Junhan Tang, Jia-Yong Wu

Publication date: 26 November 2021

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-021-01658-1

zbMATH Keywords

Busemann functionsplitting theoremBakry-Emery Ricci tensor

Mathematics Subject Classification ID

Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global Riemannian geometry, including pinching (53C20) Rigidity results (53C24)

Cites Work

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• An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature
• An extension of E. Hopf's maximum principle with an application to Riemannian geometry
• Comparison geometry for the Bakry-Emery Ricci tensor
• Two generalizations of Cheeger-Gromoll splitting theorem via Bakry-Emery Ricci curvature
• Curvature-dimension bounds for Lorentzian splitting theorems
• New restrictions on the topology of extreme black holes
• Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor
• New volume comparison results and applications to degeneration of Riemannian metrics
• The splitting theorem for manifolds of nonnegative Ricci curvature
• Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
• Recent Progress on Ricci Solitons
• The Splitting Theorem and topology of noncompact spaces with nonnegative N-Bakry Émery Ricci curvature
• A warped product version of the Cheeger-Gromoll splitting theorem