Metallic structures on tangent bundle

TL;DR

This paper investigates the properties of metallic structures on tangent bundles, focusing on their lifts, integrability, and behavior on cross-sections, contributing to differential geometry understanding.

Contribution

It introduces new fundamental formulae for metallic structures on tangent bundles and analyzes their behavior under lifts and cross-sections, expanding geometric theory.

Findings

Derived formulas for complete and horizontal lifts of metallic structures.

Analyzed integrability conditions of metallic structures on tangent bundles.

Explored behavior of metallic structures on cross-sections of tangent bundles.

Abstract

The purpose of the present work is to study the complete and horizontal lifts of the metallic structure on tangent bundles with respect to almost product structure. We also establish fundamental formulae related to integrability and horizontal lifts of metallic structures on tangent bundles. Moreover, the study revealed the behavior on cross-section of metallic structure in M to tangent bundle TM.