On twisted Riemannian extensions associated with Szabó metrics

Year 2017, Volume: 46 Issue: 4, 593 - 601, 01.08.2017

Abdoul Salam Diallo Silas Longwap Fortuné Massamba

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 $(M,\nabla)$ 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

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