Three-manifolds of constant vector curvature one. (Variétés de dimension trois à courbure vectorielle constante un.) (English. French summary) Zbl 1362.53052
Summary: A Riemannian manifold has \(\operatorname{CVC}(\epsilon)\) if its sectional curvatures satisfy \(\sec \leq \varepsilon\) or \(\sec \geq \varepsilon\) pointwise, and if every tangent vector lies in a tangent plane of curvature \(\epsilon\). We present a construction of an infinite-dimensional family of compact \(\operatorname{CVC}(1)\) three-manifolds.
MSC:
| 53C24 | Rigidity results |
| 53B20 | Local Riemannian geometry |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
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