A characterization for isometries and conformal mappings of pseudo-Riemannian manifolds |
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Authors: | Jan Peleska |
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Institution: | (1) Hochschule der Bundeswehr Hamburg, Holstenhofweg 85, D-2000 Hamburg 70, Federal Republic of Germany |
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Abstract: | Generalizing theorems of Myers-Steenrod and of Hawking, we obtain characterizations for isometries and conformal mappings of pseudo-Riemannian spaces (M, g): Define a local distance function on convex normal neighbourhoods by (p, q) =g(exp
p
–1
q, exp
p
–1
q). Then every homeomorphismf locally preserving these functions is an isometry. If (M, g) has indefinite signature andf locally preserves distance zero, it is a conformal diffeomorphism. |
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Keywords: | Primary 53B20 53B30 Secondary 53A30 83C40 |
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