A conjecture of Gromov states that if M is a compact manifold, the space of Diff(M)-orbits of curvature homogeneous metrics modeled on a fixed algebraic curvature tensor is finite-dimensional. Ben Schmidt and Jon Wolfson give a construction which assigns to each smooth positive function F on S^1, a complete and curvature homogeneous metric g_F on SL(2,R). Each metric is curvature homogeneous with curvature tensor modeled on the same algebraic curvature tensor. Moreover, two functions F and G on S^1 lie in the same Diff(S^1)-orbit if and only if the corresponding metrics g_F and g_G lie in the same Diff(SL(2,R))-orbit, hence showing the compactness assumption in Gromov's conjecture is necessary.

### Graduate Student Geometry-Topology Seminar

Wednesday, September 27, 2017 - 12:00pm

#### Sammy Sbiti

University of Pennsylvania