Three-manifolds of constant vector curvature one

Benjamin Schmidt; Jon Wolfson

doi:10.1016/j.crma.2017.03.001

Differential geometry

Three-manifolds of constant vector curvature one

Presented by: the Editorial Board

Benjamin Schmidt ¹; Jon Wolfson ¹

¹ Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

Comptes Rendus. Mathématique, Volume 355 (2017) no. 4, pp. 460-463.

Abstract
Résumé

A Riemannian manifold has $CVC (ϵ)$ if its sectional curvatures satisfy $\sec \leq ε$ or $\sec \geq ε$ 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.

Une variété riemannienne est dite $CVC (ϵ)$ si sa courbure sectionnelle satisfait ponctuellement $\sec \leq ε$ ou $\sec \geq ε$ 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 $CVC (1)$ .

Received: 2016-12-20
Accepted: 2017-03-02
Published online: 2017-03-21

DOI: 10.1016/j.crma.2017.03.001

Author's affiliations:

Benjamin Schmidt ¹; Jon Wolfson ¹

¹ Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA

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     title = {Three-manifolds of constant vector curvature one},
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     language = {en},
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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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