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.
Nous étudions la géométrie à l'infini des instantons gravitationnels, i.e. des variétés hyperkählériennes, asymptotiquement plates et de dimension quatre. En particulier, nous prouvons que les instantons gravitationnels dont la croissance de volume est cubique sont asymptotiques à une fibration en cercles au-dessus d'un espace euclidien à trois dimensions, avec des fibres de longueur asymptotiquement constante ; autrement dit, ils sont ALF (asymptotically locally flat).
Keywords: gravitational instantons, hyperkähler manifolds, asymptotically flat manifolds
Mot clés : instantons gravitationnels, variétés hyperkähleriennes, variétés asymptotiquement plates
@article{ASENS_2010_4_43_6_883_0, author = {Minerbe, Vincent}, title = {On the asymptotic geometry of gravitational instantons}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {883--924}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 43}, number = {6}, year = {2010}, doi = {10.24033/asens.2135}, mrnumber = {2778451}, zbl = {1215.53043}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/asens.2135/} }
TY - JOUR AU - Minerbe, Vincent TI - On the asymptotic geometry of gravitational instantons JO - Annales scientifiques de l'École Normale Supérieure PY - 2010 SP - 883 EP - 924 VL - 43 IS - 6 PB - Société mathématique de France UR - http://archive.numdam.org/articles/10.24033/asens.2135/ DO - 10.24033/asens.2135 LA - en ID - ASENS_2010_4_43_6_883_0 ER -
%0 Journal Article %A Minerbe, Vincent %T On the asymptotic geometry of gravitational instantons %J Annales scientifiques de l'École Normale Supérieure %D 2010 %P 883-924 %V 43 %N 6 %I Société mathématique de France %U http://archive.numdam.org/articles/10.24033/asens.2135/ %R 10.24033/asens.2135 %G en %F ASENS_2010_4_43_6_883_0
Minerbe, Vincent. On the asymptotic geometry of gravitational instantons. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 43 (2010) no. 6, pp. 883-924. doi : 10.24033/asens.2135. http://archive.numdam.org/articles/10.24033/asens.2135/
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