7 papers
A kinematic explanation of the 1:3 ratio for rolling spheres and the exceptional simple Lie group of rank two
Jacob W. Erickson
Given a pair of (round) 2-dimensional spheres, one of which has radius three times that of the other, the Lie algebra of local infinitesimal symmetries for the distribution corresp…
Inequivalence of the various notions of completeness for Cartan geometries
Jacob W. Erickson, Benjamin McKay
We demonstrate that the three prevailing notions of completeness for Cartan geometries are not actually equivalent and provide methods for constructing many examples in the affine…
Holonomy of Parabolic Geometries Near Isolated Higher-Order Fixed Points
Jacob W. Erickson
For Cartan geometries admitting an automorphism with isotropy satisfying a particular, loosely dynamical property on their model geometries, we demonstrate the existence of an open…
A method for determining Cartan geometries from the local behavior of automorphisms
Jacob W. Erickson
We introduce a construction for a Cartan geometry that captures the local behavior of a given geometric automorphism near a distinguished element. The result of this construction,…
Higher rank parabolic geometries with essential automorphisms and nonvanishing curvature
Jacob W. Erickson
We construct infinite families of regular normal Cartan geometries with nonvanishing curvature and essential automorphisms on closed manifolds for many higher rank parabolic model…
Intrinsic holonomy and curved cosets of Cartan geometries
Jacob W. Erickson
We provide an intrinsic notion of curved cosets for arbitrary Cartan geometries, simplifying the existing construction of curved orbits for a given holonomy reduction. To do this,…
Some elementary observations regarding reductive Cartan geometries
Jacob W. Erickson
After defining generalizations of the notions of covariant derivatives and geodesics from Riemannian geometry for reductive Cartan geometries in general, various results for reduct…