On the existence of pre-semigeodesic coordinates

TL;DR

This paper investigates the conditions under which pre-semigeodesic coordinates exist on manifolds with affine connection, proving their existence when the connection components are twice differentiable.

Contribution

It establishes the existence of pre-semigeodesic coordinates under the condition of twice differentiability of affine connection components.

Findings

Pre-semigeodesic coordinates exist when affine connection components are twice differentiable.

The paper provides a proof of existence for these coordinates under specified smoothness conditions.

Abstract

In the present paper we consider the problem of the existence of pre-semigeodesic coordinates on manifolds with affine connection. We proved that pre-semigeodesic coordinates exist in the case when the components of the affine connection are twice differentiable functions.