Almost Bronze Structures on Differentiable Manifolds

Abstract

This study introduces a novel structure that is not included in the metallic structure family. This new structure, which is called an almost bronze structure, has been defined using a 1,1 type tensor field φ which fulfills the requirement φ 2 = m φ − I d on a differentiable manifold. We investigated the parallelism and integrability conditions of these almost bronze structures by use of an almost product structure corresponding to them. Also, we have defined an almost bronze Riemannian manifold.

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

“…Investigating metallic structures and their subclasses (such as golden, silver, bronze etc. structures) on Riemannian manifolds is an actual subject in differential geometry (see for example [5], [11], [13,17]).…”