Test Rigid Bodies in Riemannian Spaces and Their Quantization

Discussed are some classical and quantization problems of rigid bodies of infinitesimal size moving in Riemannian spaces. The rigorous meaning of “infinitesimal size” consists in replacing an extended body by the structured material point with internal degrees of freedom (co-moving orthonormal frame). The special case of constant curvature two-dimensional spaces is discussed. The Sommerfeld polynomial method is used to perform the quantization of such problems.