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Manifolds with a non-degenerate symmetric bilinear form in each tangent space varying differentiably but with constant index and signature.

19 votes
1 answer
450 views

Lorentzian analogue to Thurston geometries

Is there an analogue to the eight Thurston geometries for Lorentz metrics? If so, how many "disctinct" geometries are there in the Lorentzian case? And which closed 3-manifolds admit metrics which a …
JS.'s user avatar
  • 893
7 votes
0 answers
245 views

Completeness is a conformal invariant

In this article about completeness of semi-riemannian manifolds the author writes (in section 2.2) that it is unkown if the following statement holds: A compact indefinite manifold which is conformal …
JS.'s user avatar
  • 893
3 votes
1 answer
282 views

Closed Semi-Riemannian manifolds with non-compact isometry group

Does anyone know a good reference for general results about closed Semi-Riemannian manifolds which have a non-compact isometry group? Edit: My goal is to understand a bit better what the intuition b …
JS.'s user avatar
  • 893