The Riemannian and Lorentzian Splitting Theorems
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Publication:4637329
DOI10.2991/978-94-6239-240-3_1zbMath1391.53044OpenAlexW2564706376MaRDI QIDQ4637329
Publication date: 18 April 2018
Published in: Topics in Modern Differential Geometry (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2991/978-94-6239-240-3_1
Busemann functionrigidity theoremscurvature inequalityLorentzian splitting theoremRiemannian splitting theorem
Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global Riemannian geometry, including pinching (53C20)
Related Items (3)
Geometry of weighted Lorentz–Finsler manifolds II: A splitting theorem ⋮ Galilean generalized Robertson-Walker spacetimes: A new family of Galilean geometrical models ⋮ On the geometry of stationary Galilean spacetimes
Cites Work
- Some results about the level sets of Lorentzian Busemann function and Bartnik's conjecture
- An extension of E. Hopf's maximum principle with an application to Riemannian geometry
- An elementary proof of the Cheeger-Gromoll splitting theorem
- A proof of the splitting conjecture of S.-T. Yau
- Splitting theorems for spatially closed space-times
- Decomposition theorems for Lorentzian manifolds with nonpositive curvature
- The splitting theorem for space-times with strong energy condition
- Remarks on cosmological spacetimes and constant mean curvature surfaces
- The Lorentzian splitting theorem without the completeness assumption
- Regularity of variational maximal surfaces
- Lines in space-times
- On complete open manifolds of positive curvature
- The splitting theorem for manifolds of nonnegative Ricci curvature
- On the structure of complete manifolds of nonnegative curvature
- Regularity of Lorentzian Busemann Functions
- Riemannian spaces which contain straight lines
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