Metallic Riemannian Structures on the Tangent Bundles of Riemannian Manifolds with $g-$Natural Metrics

Year 2023, Volume: 16 Issue: 1, 95 - 103, 30.04.2023

Murat Altunbaş

https://doi.org/10.36890/iejg.1145729

Abstract

Let $(M,g)$ be a Riemannian manifold and $(TM,\tilde{g})$ be its tangent bundle with the $g-$natural metric. In this paper, a family of metallic Riemannian structures $J$ is constructed on $TM,$ found conditions under which these structures are integrable. It is proved that $(TM,\tilde{g},J)$ is decomposable if and only if $(M,g)$ is flat.

Keywords

g-natural metric, metallic Riemannian structure, tangent bundle

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