How do we explicitly compute the curvature form $\Omega$ of the Levi-Civita connection $\nabla^{L.C.}$ for the $n$-sphere $S^n$?

Thus, how do we calculate the trace over the matrix logarithm $\log((\sigma_2 \otimes I_{n/2})^T\cdot\Omega)$ for $\sigma_2$ the second Pauli matrix, and $I_{n/2}$ the identity matrix of dimension $n/2$?

Thanks in advance! Any help would be much appreciated.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.