Structures conformes asymptotiquement plates

TL;DR

This paper explores the theory of weighted spinors on conformal manifolds, introduces asymptotically flat Weyl structures and their mass, and proves a conformal positive mass theorem.

Contribution

It extends the positive mass theorem to conformal spin manifolds by developing the theory of asymptotically flat Weyl structures.

Findings

Established a conformal positive mass theorem

Defined asymptotically flat Weyl structures and associated mass

Revisited weighted spinor theory on conformal manifolds

Abstract

In the first part of this article we revisit the theory of weighted spinors on conformal manifolds. In the second part we introduce the notions of asymptotically flat Weyl structures and of associated mass, and we prove a conformal version of the positive mass theorem on conformal spin manifolds.