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

Access to Document

10.1007/BF01781072

Cite this

@article{aad1f114afd34fb4b9d301de36be7537,

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",

month = dec,

doi = "10.1007/BF01781072",

language = "English",

volume = "135",

pages = "279--291",

journal = "Annali di Matematica Pura ed Applicata",

issn = "0373-3114",

publisher = "Springer Nature",

number = "1",

}

TY - JOUR

T1 - Local similarity manifolds

AU - Vaisman, Izu

AU - Reischer, Corina

PY - 1983/12

Y1 - 1983/12

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.

UR - http://www.scopus.com/inward/record.url?scp=0043090573&partnerID=8YFLogxK

U2 - 10.1007/BF01781072

DO - 10.1007/BF01781072

M3 - Article

AN - SCOPUS:0043090573

SN - 0373-3114

VL - 135

SP - 279

EP - 291

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

IS - 1

ER -

Local similarity manifolds

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this