The Blaschke conjecture and great circle fibrations of spheres

We construct an explicit diffeomorphism taking any fibration of a sphere by great circles into the Hopf fibration, using elementary geometry--indeed the diffeomorphism is a local (differential) invariant, algebraic in derivatives.Comment: 61 pages, 8 figures, corrected errors in the published versio

Extension Phenomena for Holomorphic Geometric Structures

The most commonly encountered types of complex analytic G-structures and Cartan geometries cannot have singularities of complex codimension 2 or more.Comment: published versio

Lifting locally homogeneous geometric structures

We prove that under some purely algebraic conditions every locally homogeneous structure modelled on some homogeneous space is induced by a locally homogeneous structure modelled on a different homogeneous space.Comment: 9 page