Phil Parker

Phil Parker, Professor

Differential Geometry, Math Physics; PhD, Oregon State University, 1977


PhD Students

Paul D. Sinclair, "Metrics on Bundle Spaces and Harmonic Gauss Map", PhD thesis, 1991


There are two main lines, one around pseudoRiemannian (indefinite metric tensor) geometries and one around (possibly nonlinear) connections associated to second-order differential equations (quasisprays). The former has lately concentrated on 2-step nilpotent Lie groups (see here for a nontechnical, historical overview), most recently on the conjugate locus and degeneracies. The latter includes a major extension of the Ambrose-Palais-Singer correspondence; see here for a more technical overview with some history.

Selected Publications