g-Natural metrics of constant sectional curvature

TL;DR

This paper characterizes when tangent bundles with g-natural metrics have constant sectional curvature, showing they are flat, and provides a detailed description of flat g-natural metrics.

Contribution

It establishes a necessary and sufficient condition for g-natural metrics on tangent bundles to have constant sectional curvature, identifying flatness as the key property, and characterizes all flat g-natural metrics.

Findings

Tangent bundle with g-natural metric has constant sectional curvature iff it is flat.

Provides a characterization of flat g-natural metrics on tangent bundles.

Shows that non-flat g-natural metrics cannot have constant sectional curvature.

Abstract

We prove that the tangent bundle endowed with a g-natural metrics has constant sectional curvature if and only if it is flat, and then we give a characterization of flat g-natural metrics on tangent bundles.