Angular momentum is a vector. It has nothing to do with the curvature of anything.

All vectors in any space can be represented by the shortest path from an origin, e.g. 40.7127° N, 74.0059° W is the vector for New York, as represented by a sector of a great circle that passes through the equator south of London. There will be an equivalent formulation for any vector in any curved space.

A straight line is unbounded so therefore a directional vector is also unbounded.

Beware of imprecise terminology. "Directional vectors", conventionally

* i,j,k *in Euclidean 3-space, are indeed bounded - they have unit length by definition, and other vectors are specified as multiples of those elements. But a

*direction*, as defined by the ratio of elements

* i,j,k,* is of course unbounded.