Department of Mathematics

Geometry and Topology

  •  Curvature free rigidity for higher rank three manifolds.
  •  10/27/2016
  •  2:00 PM - 2:50 PM
  •  C304 Wells Hall
  •  Samuel Lin, MSU

Fixing K=-1,0, or 1, a complete Riemannian manifold is said to have higher rank if each geodesic admits a parallel vector field making curvature K with the geodesic. Locally symmetric spaces provide examples. Rank rigidity theorems aim to show that these are the only examples of manifolds of higher rank, usually with additional curvature assumptions. After discussing historical results, I'll discuss how rank rigidity results hold in dimension three without additional curvature assumptions.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science