On conformally flat Lorentz parabolic manifolds

Yoshinobu Kamishima

Open Mathematics (2014)

  • Volume: 12, Issue: 6, page 861-878
  • ISSN: 2391-5455

Abstract

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We introduce conformally flat Fefferman-Lorentz manifold of parabolic type as a special class of Lorentz parabolic manifolds. It is a smooth (2n+2)-manifold locally modeled on (Û(n+1, 1), S 2n+1,1). As the terminology suggests, when a Fefferman-Lorentz manifold M is conformally flat, M is a Fefferman-Lorentz manifold of parabolic type. We shall discuss which compact manifolds occur as a conformally flat Fefferman-Lorentz manifold of parabolic type.

How to cite

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Yoshinobu Kamishima. "On conformally flat Lorentz parabolic manifolds." Open Mathematics 12.6 (2014): 861-878. <http://eudml.org/doc/269662>.

@article{YoshinobuKamishima2014,
abstract = {We introduce conformally flat Fefferman-Lorentz manifold of parabolic type as a special class of Lorentz parabolic manifolds. It is a smooth (2n+2)-manifold locally modeled on (Û(n+1, 1), S 2n+1,1). As the terminology suggests, when a Fefferman-Lorentz manifold M is conformally flat, M is a Fefferman-Lorentz manifold of parabolic type. We shall discuss which compact manifolds occur as a conformally flat Fefferman-Lorentz manifold of parabolic type.},
author = {Yoshinobu Kamishima},
journal = {Open Mathematics},
keywords = {Lorentz parabolic structure; Conformally flat Lorentz structure; Fefferman-Lorentz manifold; Uniformization; Holonomy group; Developing map; Similarity structure; conformally flat Lorentz structure; uniformization; holonomy group; developing map; similarity structure},
language = {eng},
number = {6},
pages = {861-878},
title = {On conformally flat Lorentz parabolic manifolds},
url = {http://eudml.org/doc/269662},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Yoshinobu Kamishima
TI - On conformally flat Lorentz parabolic manifolds
JO - Open Mathematics
PY - 2014
VL - 12
IS - 6
SP - 861
EP - 878
AB - We introduce conformally flat Fefferman-Lorentz manifold of parabolic type as a special class of Lorentz parabolic manifolds. It is a smooth (2n+2)-manifold locally modeled on (Û(n+1, 1), S 2n+1,1). As the terminology suggests, when a Fefferman-Lorentz manifold M is conformally flat, M is a Fefferman-Lorentz manifold of parabolic type. We shall discuss which compact manifolds occur as a conformally flat Fefferman-Lorentz manifold of parabolic type.
LA - eng
KW - Lorentz parabolic structure; Conformally flat Lorentz structure; Fefferman-Lorentz manifold; Uniformization; Holonomy group; Developing map; Similarity structure; conformally flat Lorentz structure; uniformization; holonomy group; developing map; similarity structure
UR - http://eudml.org/doc/269662
ER -

References

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