Hypersurfaces of semi-Riemannian conformally flat manifolds. (English) Zbl 0731.53021
Geometry and topology III, Proc. Workshop, Leeds/UK 1990, 131-147 (1991).
[For the entire collection see Zbl 0724.00015.]
Let \(M_{n+1}(c)\) be a semi-Riemannian manifold of constant curvature c, and let (N,g) be an isometrically immersed hypersurface of \(M_{n+1}(c)\). The authors prove a number of interesting properties of those hypersurfaces, i.e. every Einstein hypersurface (N,g) in \(M_{n+1}(c)\) is pseudo-symmetric. E. Cartan and J. Schouten proved that a hypersurface of a conformally flat Riemannian manifold of dimension \(\geq 5\) is conformally flat if and only if it is quasi-umbilical, and the authors prove similar results for semi-Riemannian manifolds.
Let \(M_{n+1}(c)\) be a semi-Riemannian manifold of constant curvature c, and let (N,g) be an isometrically immersed hypersurface of \(M_{n+1}(c)\). The authors prove a number of interesting properties of those hypersurfaces, i.e. every Einstein hypersurface (N,g) in \(M_{n+1}(c)\) is pseudo-symmetric. E. Cartan and J. Schouten proved that a hypersurface of a conformally flat Riemannian manifold of dimension \(\geq 5\) is conformally flat if and only if it is quasi-umbilical, and the authors prove similar results for semi-Riemannian manifolds.
Reviewer: A.Bucki (Williamsport)
MSC:
| 53B25 | Local submanifolds |
| 53B30 | Local differential geometry of Lorentz metrics, indefinite metrics |
