Pseudo-Riemannian metrics with prescribed scalar curvature

Details Pseudo-Riemannian metrics with prescribed scalar curvature Pseudo-Riemannian metrics with prescribed scalar curvature

2004-09-22

arxiv.org/abs/math/0409435v2

Mathematics

Differential Geometry

172 pages, 1 figure

Scientific paper

We consider the following generalisation of a well-known problem in Riemannian geometry: When is a smooth real-valued function s on a given compact n-dimensional manifold M (with or without boundary) the scalar curvature of some smooth pseudo-Riemannian metric of index q on M? We prove that this is the case for every s if 2

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