Local similarity manifolds

Izu Vaisman; Corina Reischer

doi:10.1007/BF01781072

Local similarity manifolds

Izu Vaisman
, Corina Reischer

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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={ht₀^k|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 language	English
Pages (from-to)	279-291
Number of pages	13
Journal	Annali di Matematica Pura ed Applicata
Volume	135
Issue number	1
DOIs	https://doi.org/10.1007/BF01781072
State	Published - Dec 1983

ASJC Scopus subject areas

Applied Mathematics

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10.1007/BF01781072

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title = "Local similarity manifolds",

abstract = "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.",

author = "Izu Vaisman and Corina Reischer",

year = "1983",

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doi = "10.1007/BF01781072",

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journal = "Annali di Matematica Pura ed Applicata",

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N2 - 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.

AB - 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.

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DO - 10.1007/BF01781072

M3 - Article

AN - SCOPUS:0043090573

SN - 0373-3114

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EP - 291

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

IS - 1

ER -

Local similarity manifolds

Abstract

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