
# The orthonormal basis in a tangent space

Since the dimension of $\mathbb S^1$ is 1, there is only one direction ($1$), and this direction is along the geodesic, hence the “curvature” is just zero.

### Matlab Documentation

 1 2 3 4 5 6 7 8 9 10 11 12 13 % [V,k] = TpMONB(p,q) an onb of the tangent space including log_pq % since on S1 there is only one direction, this is always % included and 1; the curvature coefficients are all zero, since % this is always along the geodesic % % INPUT % p,q : two point(sets) of cyclic data % % OUTPUT % Xi : basiscolumn matrice(s). % k : (optional) curvature coefficients, here all are 0. % --- % MVIRT 1.0, R. Bergmann ~ 2018-03-03