On the scalar curvature of hypersurfaces in spaces with a Killing field
-
Alma L. Albujer
Abstract
We consider compact hypersurfaces in an (n + 1)-dimensional either Riemannian or Lorentzian space 
endowed with a conformal Killing vector field. For such hypersurfaces, we establish an integral formula which, especially in the simpler case when 
is a product space, allows us to derive some interesting consequences in terms of the scalar curvature of the hypersurface. For instance, when n = 2 and 
is either the sphere 
or the real projective plane 
, we characterize the slices of the trivial totally geodesic foliation 
as the only compact two-sided surfaces with constant Gaussian curvature in the Riemannian product 
such that its angle function does not change sign. When n ≥ 3 and 
is a compact Einstein Riemannian manifold with positive scalar curvature, we also characterize the slices as the only compact two-sided hypersurfaces with constant scalar curvature in the Riemannian product 
whose angle function does not change sign. Similar results are also established for spacelike hypersurfaces in a Lorentzian product đť•„ Ă— â„ť1.
© de Gruyter 2010
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Articles in the same Issue
- On the characteristic direction of real hypersurfaces in and a symmetry result
- Small maximal partial spreads in classical finite polar spaces
- On antipodes on a convex polyhedron II
- On the quadratic normality and the triple curve of three-dimensional subvarieties of
- A generalization of the Giulietti–Korchmáros maximal curve
- Busemann Functions and the Julia–Wolff–Carathéodory Theorem for polydiscs
- Generalized polygons with non-discrete valuation defined by two-dimensional affine â„ť-buildings
- Measures on the space of convex bodies
- On the scalar curvature of hypersurfaces in spaces with a Killing field
- The real quadrangle of type E6
- Triple-point defective surfaces
- On surfaces with pg = 2q – 3
- A counter example to an ideal membership test
