Comptes Rendus
no. 4
Differential geometry
Area minimizing projective planes on the projective space of dimension 3 with the Berger metric
[Plans projectifs minimisant l'aire dans l'espace projectif à dimension 3 muni de la métrique de Berger]

Présenté par : the Editorial Board

Olga Gil-Medrano1 
1 Faculty of Mathematics, University of Valencia, Avda. Dr. Moliner, 50, 46100 Burjassot, Valencia, Spain
Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 415-417.

On démontre que, parmi les plans projectifs dans l'espace projectif réel RP3, muni de la métrique de Berger, ceux qui réalisent le minimum de l'aire sont exactement ceux qu'on obtient par la projection des sphères équatoriales de S3. Le résultat généralise un résultat classique pour l'espace projectif muni de la métrique ordinaire.

We show that, among the projective planes embedded into the real projective space RP3 endowed with the Berger metric, those of least area are exactly the ones obtained by projection of the equatorial spheres of S3. This result generalizes a classical result for the projective spaces with the standard metric.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.12.011
Olga Gil-Medrano 1

1 Faculty of Mathematics, University of Valencia, Avda. Dr. Moliner, 50, 46100 Burjassot, Valencia, Spain 
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Olga Gil-Medrano. Area minimizing projective planes on the projective space of dimension 3 with the Berger metric. Comptes Rendus. Mathématique, Volume 354 (2016) no. 4, pp. 415-417. doi : 10.1016/j.crma.2015.12.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.12.011/

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