Geometric Formulation of 4-Dimensional Space via Central Projection

This report examines, from a purely geometric perspective, the deformation of the induced metric that arises in the coordinate system after mapping a 4-dimensional Euclidean space (tangent hyperplane Π_R) onto the surface of a 5-dimensional hypersphere of curvature radius R via central projection. In particular, we demonstrate step by step: (i) the exact derivation of the induced metric tensor g_μν after the mapping (including the contribution of the 5th component), and (ii) the geometric relationship between the Einstein tensor and the constant Λ = 3/R². This report excludes all cosmological assumptions.