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Constante Systolique Et Variétés Plates by El Mir-C

Constante Systolique Et Variétés Plates

by El Mir-C
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Book cover type: Paperback
  • ISBN13: 9786131553929
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Omniscriptum
  • Publisher Imprint: Omniscriptum
  • Publication Date:
  • Pages: 72
  • Original Price: GBP 25.0
  • Language: French
  • Edition: N/A
  • Item Weight: 118 grams
  • BISAC Subject(s): Geometry / General

Dans cette thèse on étudie la géométrie systolique des variétés de Bieberbach. La systole d'une variété riemannienne compacte et non simplement connexe est l'infimum des longueurs des courbes fermées non contractiles; le rapport systolique est le quotient de la systole à la puissance la dimension par le volume. Un résultat fondamental de Gromov assure que si la variété est essentielle, le quotient systolique reste fini si la métrique varie. Les surfaces compactes autres que la sphère sont essentielles, et le théorème de Gromov est une généralisation profonde des mèmes résultats pour le tore de dimension 2 (C. Loewner), pour le plan projectif (M. Pu) et pour la bouteille de Klein (C. Bavard). Pour ces variétés la constante systolique est bien connu mais en dimension supérieure, on ne connait pratiquement rien en dehors de l'existence de cette constante. Nous nous intéressons aux variétés de Bieberbach de dimension 3, c'est à dire aux variétés compactes de dimension 3 qui portent une métrique riemannienne plate, qui ne sont pas des tores et démontrons que les métriques plates ne sont pas optimales pour le rapport systolique.

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