Projectively Flat Affine Surfaces That are Not Locally Symmetric

On a class of locally projectively flat Finsler metrics

‎In this paper we study Finsler metrics with orthogonal invariance‎. ‎We‎ ‎find a partial differential equation equivalent to these metrics being locally projectively flat‎. ‎Some applications are given‎. ‎In particular‎, ‎we give an explicit construction of a new locally projectively flat Finsler metric of vanishing flag curvature which differs from the Finsler metric given by Berwald in 1929.

Hyperbolic Sets That are Not Locally Maximal

This papers addresses the following topics relating to the structure of hyperbolic sets: First, hyperbolic sets that are not contained in locally maximal hyperbolic sets. Second, the existence of a Markov partition for a hyperbolic set. We construct new examples of hyperbolic sets which are not contained in locally maximal hyperbolic sets. The first example is robust under perturbations and can...

Constructing Complete Projectively Flat Connections

Theorem 1. Let T 2 be the two dimensional torus. Then for any positive integer m there is a complete torsion free projectively flat connection, ∇, on T 2 such that for any point p ∈ T 2 there is a point q ∈ T 2 with the property that any broken ∇-geodesic between p and q has at least m breaks. Moreover if T 2 is viewed as a Lie group in the usual manner, this connection is invariant under trans...

Surfaces with Degenerate Cr Singularities That Are Locally Polynomially Convex

A compact subset K ⊂ C is said to be polynomially convex if for every point ζ / ∈ K, there exists a holomorphic polynomial P such that P (ζ) = 1 and supK |P | < 1. K is said to be locally polynomially convex at a point p ∈ K if there exists a closed ball B(p) centered at p such that K ∩ B(p) is polynomially convex. In general, it is difficult to determine whether a given compact K ⊂ C is polyno...

74 the Deformation Spaces of Projectively Flat