On the Riemannian Geometry of the Cayley Projective Plane

Brian Van Koten
Lewis and Clark College

Abstract: In a painting done in perspective, every pair of lines, even parallel lines, intersects at a single point. For example, envision railroad tracks receding into the distance. This notion of perspective gave birth to a type of non-Euclidean geometry called projective geometry. I will discuss a related family of spaces called projective planes which are of current interest to differential geometers since they belong to a small class of spaces with certain very nice symmetries. Specifically, I will discuss natural ways to view projective planes as Riemannian manifolds and how it is possible to relate different models of the Cayley projective plane.