This analysis demonstrates that the ground eigenvalue equals the surface scalar curvature in a Möbius band, indicating implications for cosmological constants.
We establish that the ground eigenvalue of the twisted Laplace-Beltrami operator on a Möbius band, embedded totally geodesically in S³, equals the surface scalar curvature exactly: λ₀ = R_Σ = 2/R² Two independent paths (direct Rayleigh quotient and Bochner lower bound) yield the same result, with geodesic boundaries ensuring vanishing flux. The curvature of S³ supplies a factor of 2 over the flat-strip value. To the authors' knowledge this specific model has not received prior treatment. The result grounds the topological derivation of the cosmological constant in Mode Identity Theory.
No takes yet. Share an insight, caveat, or question.
Blake Shatto (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: