On the asymptotic geometry of gravitational instantons

Vincent Minerbe

Annales scientifiques de l'École Normale Supérieure (2010)

  • Volume: 43, Issue: 6, page 883-924
  • ISSN: 0012-9593

Abstract

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We investigate the geometry at infinity of the so-called “gravitational instantons”, i.e. asymptotically flat hyperkähler four-manifolds, in relation with their volume growth. In particular, we prove that gravitational instantons with cubic volume growth are ALF, namely asymptotic to a circle fibration over a Euclidean three-space, with fibers of asymptotically constant length.

How to cite

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Minerbe, Vincent. "On the asymptotic geometry of gravitational instantons." Annales scientifiques de l'École Normale Supérieure 43.6 (2010): 883-924. <http://eudml.org/doc/272146>.

@article{Minerbe2010,
abstract = {We investigate the geometry at infinity of the so-called “gravitational instantons”, i.e. asymptotically flat hyperkähler four-manifolds, in relation with their volume growth. In particular, we prove that gravitational instantons with cubic volume growth are ALF, namely asymptotic to a circle fibration over a Euclidean three-space, with fibers of asymptotically constant length.},
author = {Minerbe, Vincent},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {gravitational instantons; hyperkähler manifolds; asymptotically flat manifolds},
language = {eng},
number = {6},
pages = {883-924},
publisher = {Société mathématique de France},
title = {On the asymptotic geometry of gravitational instantons},
url = {http://eudml.org/doc/272146},
volume = {43},
year = {2010},
}

TY - JOUR
AU - Minerbe, Vincent
TI - On the asymptotic geometry of gravitational instantons
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2010
PB - Société mathématique de France
VL - 43
IS - 6
SP - 883
EP - 924
AB - We investigate the geometry at infinity of the so-called “gravitational instantons”, i.e. asymptotically flat hyperkähler four-manifolds, in relation with their volume growth. In particular, we prove that gravitational instantons with cubic volume growth are ALF, namely asymptotic to a circle fibration over a Euclidean three-space, with fibers of asymptotically constant length.
LA - eng
KW - gravitational instantons; hyperkähler manifolds; asymptotically flat manifolds
UR - http://eudml.org/doc/272146
ER -

References

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