Levi-Civita connection for $SU_q(2)$

TL;DR

This paper establishes the existence and uniqueness of a Levi-Civita connection on the quantum group $SU_q(2)$ for certain calculi and metrics, advancing the understanding of quantum geometry structures.

Contribution

It proves a metric-independent condition ensuring a unique bicovariant Levi-Civita connection on $SU_q(2)$, a significant step in quantum differential geometry.

Findings

Existence of a unique Levi-Civita connection for $SU_q(2)$

Applicable to $4D_ abla$ calculi and bi-invariant metrics

Provides a metric-independent criterion for Levi-Civita connections

Abstract

We prove that the $4D_\pm$ calculi on the quantum group $SU_q(2)$ satisfy a metric-independent sufficient condition for the existence of a unique bicovariant Levi-Civita connection corresponding to every bi-invariant pseudo-Riemannian metric.