Geodesics in Conical Manifolds

TL;DR

This paper extends the concept of geodesics to conical manifolds with singularities, developing a framework for local and variational analysis in such spaces.

Contribution

It introduces a new approach to defining and analyzing geodesics on conical manifolds, accommodating singularities within the variational calculus.

Findings

Established a generalized definition of geodesics on conical manifolds.

Developed methods for local geodesic problem in singular spaces.

Provided a variational framework suitable for conical manifolds.

Abstract

The aim of this paper is to extend the definition of geodesics to conical manifolds, defined as submanifolds of $\R^n$ with a finite number of singularities. We look for an approach suitable both for the local geodesic problem and for the calculus of variation in the large