# Invariants topologiques pour le problème de la courbure scalaire sur les variétés

## Topological invariants for the scalar curvature problem on manifolds

King Abdulaziz University
Saudi Arabia

Hichem Chtioui
Sfax University
Tunisia

Publié le 7 mars 2023   DOI : 10.21494/ISTE.OP.2023.0936

### Keywords

In [7], A.Bahri introduced two topological invariants μ and τ to study the prescribed scalar curvature problem on standard spheres of high dimensions. In this paper we first extend μ and τ to the problem on general riemannian manifolds. Second we analyze, as suggested in [7], the relation between these two quantities and we prove under topological conditions that μ = τ.

In [7], A.Bahri introduced two topological invariants μ and τ to study the prescribed scalar curvature problem on standard spheres of high dimensions. In this paper we first extend μ and τ to the problem on general riemannian manifolds. Second we analyze, as suggested in [7], the relation between these two quantities and we prove under topological conditions that μ = τ.