## 3 Citations

### Levi-Civita connection for $SU_q(2)$

- Mathematics
- 2020

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…

### Metric compatibility and Levi-Civita Connections on Quantum Groups

- Mathematics
- 2022

Arbitrary right connections on bicovariant bimodules of a quantum group (Hopf algebra) are shown to canonically extend to tensor products of bicovariant bimodules. In particular, a connection on a…

### Pseudo-Riemannian metrics on bicovariant bimodules

- Mathematics
- 2019

We study pseudo-Riemannian invariant metrics on bicovariant bimodules over Hopf algebras. We clarify some properties of such metrics and prove that pseudo-Riemannian invariant metrics on a…

## References

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### Noncommutative Principal Bundles Through Twist Deformation

- Mathematics
- 2016

We construct noncommutative principal bundles deforming principal bundles with a Drinfeld twist (2-cocycle). If the twist is associated with the structure group then we have a deformation of the…

### Schmüdgen : Levi-Civita Connections on the Quantum Groups SLq(N) Oq(N) and Sp q (N)

- Comm. Math. Phys. 185,
- 1997

### Pseudo-Riemannian metrics on bicovariant bimodules

- Mathematics
- 2019

We study pseudo-Riemannian invariant metrics on bicovariant bimodules over Hopf algebras. We clarify some properties of such metrics and prove that pseudo-Riemannian invariant metrics on a…

### Differential calculus on compact matrix pseudogroups (quantum groups)

- Mathematics
- 1989

The paper deals with non-commutative differential geometry. The general theory of differential calculus on quantum groups is developed. Bicovariant bimodules as objects analogous to tensor bundles…

### Noncommutative Geometry

- Mathematics
- 1997

Noncommutative Spaces It was noticed a long time ago that various properties of sets of points can be restated in terms of properties of certain commutative rings of functions over those sets. In…

### A new look at Levi-Civita connection in noncommutative geometry

- Mathematics
- 2016

We prove the existence and uniqueness of Levi-Civita connections for a noncommutative pseudo-Riemannian metric on a class of centered bimodule of one forms. As an application, we compute the Ricci…

### On the Koszul formula in noncommutative geometry

- MathematicsReviews in Mathematical Physics
- 2020

We prove a Koszul formula for the Levi-Civita connection for any pseudo-Riemannian bilinear metric on a class of centered bimodule of noncommutative one-forms. As an application to the Koszul…