On geodesic mappings of manifolds with affine connection

TL;DR

This paper proves that any manifold with an affine connection can be globally transformed into an equiaffine manifold characterized by a symmetric Ricci tensor, establishing a universal projective equivalence.

Contribution

It demonstrates that all manifolds with affine connections are globally projectively equivalent to equiaffine manifolds, a novel unification in affine geometry.

Findings

All affine manifolds are globally projectively equivalent to equiaffine manifolds.

Equiaffine manifolds are characterized by symmetric Ricci tensors.

The result provides a universal link between affine and equiaffine geometries.

Abstract

In this paper we prove that all manifolds with affine connection are globally projectively equivalent to some space with equiaffine connection (equiaffine manifold). These manifolds are characterised by a symmetric Ricci tensor.