Summary
A local similarity manifold is defined as a locally affine manifold for which the transition functions of an affine atlas are similarity transformations inR n. The main result of this paper is that, for n≧3, the compact local similarity manifolds (which are not locally Euclidean) are given by the formula M=(R n{0} G, where G is a group of covering transformations such that G={ht k0 ¦h ε H, k εZ, H being a finite orthogonal group without fixed points inR n{0},and t0 being some conformal linear transformation ofR n which commutes with H.
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This work was supported by the N.S.E.R.C. Canada, grant A4063.
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Vaisman, I., Reischer, C. Local similarity manifolds. Annali di Matematica pura ed applicata 135, 279–291 (1983). https://doi.org/10.1007/BF01781072
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DOI: https://doi.org/10.1007/BF01781072