Abstract
Let M= M n, m be the Euclidean space R p equipped with a symmetric bilinear form B M of rank p= n+ m and signature n− m. We compactify M so that M c is homogeneous and has as its group of isometries a Lie group whose dimension is the dimension of M plus 2 p+1. We observe that M c is in two ways the total space of a non-trivial sphere bundle with base space real projective space. The compactification is well understood in the classical case when M is Minkowski space. The contribution here is to observe that the construction works generally and that it admits a natural bundle description.
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