Levi-Civita connection for $SU_q(2)$

preprint2020arXivOpen access

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.

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Levi-Civita connection for $SU_q(2)$

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Levi-Civita connection for SUq(2)SU_q(2)SUq​(2)

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Levi-Civita connection for $SU_q(2)$