Closed Surface Pattern Curvature Tensor: A Geometric Framework for Electron Shell Structure

This study introduces the Closed Surface Pattern Curvature Tensor F_Φ,it,it as a fundamental geometrical tool for describing electron shell structure. By modeling the electron as a modulated closed surface rather than a point particle, the theory captures orbital discreteness, repulsion dynamics, and energy quantization through surface pattern gradients. The framework leverages spherical harmonics to express pattern modes and demonstrates how curvature-induced repulsion balances Coulomb attraction to yield stable orbital radii. This approach provides a unified geometric model that bridges quantum mechanics with surface differential geometry. Author Tetsuo Konno(今野哲夫)https://orcid.org/0009-0002-1842-7865