Topology Seminar

Wednesday, September 27, 2017
4:20 PM - 5:20 PM (ET)
Exley Science Center Tower ESC 638
Event Type
Canalia, Caryn

Speaker: Samuel Lin, Dartmouth

Title:  Curvature Free Rigidity of Higher Rank Three-manifolds

Abstract: Fixing K=-1, 0, or 1, a Riemannian manifold (M, g) is said to have higher hyperbolic, spherical, or Euclidean rank if every geodesic in M admits a normal parallel field making curvature K with the geodesic. Rank rigidity results, which usually involve a priori sectional curvature bounds, characterize locally symmetric spaces in terms of these geometric notions of rank. 

After giving a short survey of historical results, I’ll discuss how rank rigidity holds in dimension three without a priori sectional curvature bounds.

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