Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Drew Sills**, Rutgers University, asills {at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Some applications of the cosine law in low-dimensional geometry

Speaker: ** Feng Luo**, Rutgers University

Date: Thursday, March 23, 2006 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

In the discrete approach to smooth metrics on surfaces, the basic building blocks are sometimes taken to be triangles in constant curvature spaces. In this setting edge lengths and inner angles of triangles correspond to the metrics and its curvatures. For triangles in hyperbolic, spherical and Euclidean geometries, edge lengths and inner angles are related by the cosine law. Thus cosine law should be considered as the metric-curvature relation. From this point of view, the derivative of the cosine law is an analogy of the Bianchi identity in Riemannian geometry. This talk is focus on many applications of the derivative cosine law. It provides a unification of many known approaches of constructing constant curvature metrics on surfaces. These include the work of Colin de Vedierer, Greg Leibon, Bragger, Chow and myself on variational approaches and discrete curvature flows on triangulated surfaces.