Intrinsic Curvatures of Atomic Orbitals for Hydrogen-Like Atoms

Within the quantum model for the hydrogen-like atom and taking into account the concepts of differential geometry, we calculate the intrinsic curvature of several types of atomic orbitals. Based on this concept of intrinsic curvature, a classification of atomic orbitals (AO) is given. We conclude by discussing the advantages of characterizing atomic quantum states by intrinsic curves for the AO of the hydrogen-like atom.