On the asymptotic geometry of gravitational instantons  [ Sur la géométrie asymptotique des instantons gravitationnels ]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 43 (2010) no. 6, p. 883-924
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).
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.
DOI : https://doi.org/10.24033/asens.2135
Classification:  53C20,  53C21,  53C23,  53C26,  53C29
Mots 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},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 43},
     number = {6},
     year = {2010},
     pages = {883-924},
     doi = {10.24033/asens.2135},
     zbl = {1215.53043},
     mrnumber = {2778451},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2010_4_43_6_883_0}
}
Minerbe, Vincent. On the asymptotic geometry of gravitational instantons. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 43 (2010) no. 6, pp. 883-924. doi : 10.24033/asens.2135. http://www.numdam.org/item/ASENS_2010_4_43_6_883_0/

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