# Smooth Riemannian Structures on Dessins d'Enfants

## TL;DR

This paper introduces a canonical Riemannian metric on dessins d'enfants on topological surfaces, providing a geometric explanation for a claim by Grothendieck.

## Contribution

It defines a natural Riemannian structure on dessins d'enfants, linking combinatorial and geometric aspects in a novel way.

## Key findings

- Established a canonical Riemannian metric on dessins d'enfants
- Provided a geometric interpretation of Grothendieck's claim
- Bridged combinatorial and geometric structures in topology

## Abstract

We show how to define a canonical Riemannian metric on a "dessin d'enfants' drawn on a topological surface. This gives a possible explanation of a claim of A. Grothendieck.