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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue 2 (Special CSMT 2022)   > Article

Topological invariants for the scalar curvature problem on manifolds

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


Khadijah Abdullah Sharaf
King Abdulaziz University
Saudi Arabia

Hichem Chtioui
Sfax University
Tunisia



Published on 7 March 2023   DOI : 10.21494/ISTE.OP.2023.0936

Abstract

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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.

Scalar curvature Yamabe flow Bahri’s topological invariants

Scalar curvature Yamabe flow Bahri’s topological invariants