On twisted Riemannian extensions associated with Szabó metrics

Authors : Abdoul Salam Diallo, Silas Longwap, Fortuné Massamba

Pages : 593-601

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Publication Date : 2017-08-01

Article Type : Research Paper

Abstract :Let $M$ be an n-dimensional manifold with a torsion free afine connection $\nabla$ and let $T^*M$ be the cotangent bundle. In this paper, we consider some of the geometric aspects of a twisted Riemannian extension which provide a link between the afine geometry of $insert ignore into journalissuearticles values(M,\nabla);$ and the neutral signature pseudo-Riemannian geometry of $T^*M$. We investigate the spectral geometry of the Szabó operator on $M$ and on $T^*M$.
Keywords : Afine connection, Cyclic parallel, Szabó manifold, Twisted Riemannian extension