Killing vector field of the metric II+III on Tangent Bundle

TL;DR

This paper investigates the properties of Killing vector fields on the tangent bundle of a Riemannian manifold equipped with a specific metric, extending understanding of symmetries in geometric structures.

Contribution

It provides a detailed analysis of Killing vector fields on tangent bundles with the combined metric II+III, highlighting new geometric insights.

Findings

Characterization of Killing vector fields on T(M) with metric II+III

Conditions under which these vector fields preserve the metric

Extension of known results to new metric structures

Abstract

The main purpose of the paper is to investigate Killing vector field on the tangent bundle T(M_{n}) of the Riemannian manifold with respect to the Levi-Civita connection of the metric II+III .