On the Limits of the Curvature Radius in Central Projection — The Cases R → ∞ and R → 0

Key Points

• The aim is to explore the geometric implications of extreme limits of curvature radius in central projection.
• Analyzed the structural behavior of central projection in limits R → ∞ and R → 0.
• Utilized geometric frameworks established in prior work.
• Constructed a nested structure of subjective spaces to resolve identified tensions.
• Both limits R → ∞ and R → 0 exhibit geometrically regular behavior.
• A structural tension was identified between geodesic deviation upper bounds and local curvature.
• Proposition 4.1 demonstrates that a nested structure can alleviate this tension.

Abstract