Local similarity manifolds

Izu Vaisman, Corina Reischer

Research output: Contribution to journalArticlepeer-review


A local similarity manifold is defined as a locally affine manifold for which the transition functions of an affine atlas are similarity transformations in Rn. 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=(Rn{0} G, where G is a group of covering transformations such that G={ht0k|h ε H, k εZ, H being a finite orthogonal group without fixed points in Rn{0}, and t0 being some conformal linear transformation of Rn which commutes with H.

Original languageEnglish
Pages (from-to)279-291
Number of pages13
JournalAnnali di Matematica Pura ed Applicata
Issue number1
StatePublished - Dec 1983

ASJC Scopus subject areas

  • Applied Mathematics


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