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- W2013527587 abstract "Suppose that ( M, g ) and ( M ′, g ′) are Lorentz manifolds, and that f : M → M ′ is a bijection, such that f and f -1 preserve spacelike paths ( f : M → M ′ has this property, if for any spacelike path γ: J → M in ( M ,g ), the composition f γ: J → M ′ is a spacelike path in ( M ′, g ′)). Then f is a (manifold-) homeomorphism. This statement is the ‘spacelike’ version of an analogous ‘timelike’ theorem (Hawking, King and McCarthy [6] and Göbel [2] for strongly causal, and Malament [10] for general Lorentz manifolds). With this result it is possible to prove a conjecture of Göbel [3] which states that every bijection between time-orientable n -dimensional ( n ⩾ 3) Lorentz manifolds which preserves spacelike paths is a conformal C ∞ -diffeomorphism." @default.
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- W2013527587 date "1985-07-01" @default.
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- W2013527587 title "On bijections of Lorentz manifolds, which leave the class of spacelike paths invariant" @default.
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