Lorentzian similarity manifolds

Yoshinobu Kamishima

Open Mathematics (2012)

  • Volume: 10, Issue: 5, page 1771-1788
  • ISSN: 2391-5455

Abstract

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An (m+2)-dimensional Lorentzian similarity manifold M is an affine flat manifold locally modeled on (G,ℝm+2), where G = ℝm+2 ⋊ (O(m+1, 1)×ℝ+). M is also a conformally flat Lorentzian manifold because G is isomorphic to the stabilizer of the Lorentzian group PO(m+2, 2) of the Lorentz model S m+1,1. We discuss the properties of compact Lorentzian similarity manifolds using developing maps and holonomy representations.

How to cite

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Yoshinobu Kamishima. "Lorentzian similarity manifolds." Open Mathematics 10.5 (2012): 1771-1788. <http://eudml.org/doc/269359>.

@article{YoshinobuKamishima2012,
abstract = {An (m+2)-dimensional Lorentzian similarity manifold M is an affine flat manifold locally modeled on (G,ℝm+2), where G = ℝm+2 ⋊ (O(m+1, 1)×ℝ+). M is also a conformally flat Lorentzian manifold because G is isomorphic to the stabilizer of the Lorentzian group PO(m+2, 2) of the Lorentz model S m+1,1. We discuss the properties of compact Lorentzian similarity manifolds using developing maps and holonomy representations.},
author = {Yoshinobu Kamishima},
journal = {Open Mathematics},
keywords = {Lorentzian similarity structure; Conformally flat Lorentzian structure; Uniformization; Holonomy group; Developing map; Lorentzian similarity manifold; Lorentzian flat space form; Fefferman-Lorentz manifold; developing map; holonomy representation},
language = {eng},
number = {5},
pages = {1771-1788},
title = {Lorentzian similarity manifolds},
url = {http://eudml.org/doc/269359},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Yoshinobu Kamishima
TI - Lorentzian similarity manifolds
JO - Open Mathematics
PY - 2012
VL - 10
IS - 5
SP - 1771
EP - 1788
AB - An (m+2)-dimensional Lorentzian similarity manifold M is an affine flat manifold locally modeled on (G,ℝm+2), where G = ℝm+2 ⋊ (O(m+1, 1)×ℝ+). M is also a conformally flat Lorentzian manifold because G is isomorphic to the stabilizer of the Lorentzian group PO(m+2, 2) of the Lorentz model S m+1,1. We discuss the properties of compact Lorentzian similarity manifolds using developing maps and holonomy representations.
LA - eng
KW - Lorentzian similarity structure; Conformally flat Lorentzian structure; Uniformization; Holonomy group; Developing map; Lorentzian similarity manifold; Lorentzian flat space form; Fefferman-Lorentz manifold; developing map; holonomy representation
UR - http://eudml.org/doc/269359
ER -

References

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