# Scalar Curvature of a Levi-Civita Connection on Cuntz algebra with three generators

## TL;DR

This paper introduces a differential calculus on the Cuntz algebra with three generators, establishes the existence of a Levi-Civita connection, and computes its scalar curvature for a canonical metric.

## Contribution

It constructs a differential calculus on a specific Cuntz algebra and explicitly computes the scalar curvature of its Levi-Civita connection, extending noncommutative geometry methods.

## Key findings

- Differential calculus satisfies key assumptions enabling Levi-Civita connection
- Unique Levi-Civita connection exists for the algebra with the given metric
- Scalar curvature computed explicitly for the canonical metric

## Abstract

A differential calculus on Cuntz algebra with three generators coming from the action of rotation group in three dimensions is introduced. The differential calculus is shown to satisfy Assumptions I-IV of [1] so that Levi-Civita Connection exists uniquely for any pseudo-Riemannian metric in the sense of [1]. Scalar curvature is computed for the Levi-Civita connection corresponding to the canonical bilinear metric.