Comptes Rendus
no. 4
Differential geometry
Three-manifolds of constant vector curvature one
[Variétés de dimension trois à courbure vectorielle constante un]

Présenté par : the Editorial Board

Benjamin Schmidt1 ; Jon Wolfson1
1 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Comptes Rendus. Mathématique, Volume 355 (2017) no. 4, pp. 460-463.

Une variété riemannienne est dite CVC(ϵ) si sa courbure sectionnelle satisfait ponctuellement sec≤ε ou sec≥ε et si chaque vecteur tangent appartient à un plan tangent de courbure ε. Nous construisons une famille de dimension infinie de variétés compactes de dimension 3, qui sont CVC(1).

A Riemannian manifold has CVC(ϵ) if its sectional curvatures satisfy sec≤ε or sec≥ε pointwise, and if every tangent vector lies in a tangent plane of curvature ε. We present a construction of an infinite-dimensional family of compact CVC(1) three-manifolds.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.03.001
Benjamin Schmidt 1 ; Jon Wolfson 1

1 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA 
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Benjamin Schmidt; Jon Wolfson. Three-manifolds of constant vector curvature one. Comptes Rendus. Mathématique, Volume 355 (2017) no. 4, pp. 460-463. doi : 10.1016/j.crma.2017.03.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.03.001/

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