**Authors:** Akindele J. Adekugbe

Graphical analysis of the geometry of a curved 'three-dimensional' absolute intrinsic
metric space, (an absolute intrinsic Riemannian metric space) φM^{3}, which is curved
onto the absolute time/absolute intrinsic time 'dimensions' (along the vertical), as a
curved hyper-surface, and projects a flat three-dimensional proper intrinsic metric space
φE'^{3} underlying its outward manifestation namely, the flat proper physical Euclidean
3-space φE'^{3}, both as flat hyper-surfaces along the horizontal, isolated in part one of this
paper, is done. Two absolute intrinsic tensor equations, one of which is of the divergenceless
form of Einstein free-space field equations and the other which is a tensorial
statement of local Euclidean invariance on φM^{3}, are derived. Simultaneous (algebraic)
solution of the equations yields the absolute intrinsic metric tensor and absolute intrinsic
Ricci tensor of absolute intrinsic Riemann geometry on the curved absolute intrinsic
metric space φM^{3}, in terms of an isolated absolute intrinsic curvature parameter.
Relations for absolute intrinsic coordinate projections into the underlying flat proper
intrinsic space are derived. A superposition procedure that yields resultant absolute intrinsic
metric tensor and resultant absolute intrinsic Ricci tensor, as well as resultant
absolute intrinsic coordinate projection relations when two or a larger number of absolute
intrinsic Riemannian metric spaces co-exist, are developed. Finally the fact that
a curved 'three-dimensional' absolute intrinsic metric space φM^{3} is perfectly isotropic
(that is, all directions are perfectly the same) and is consequently contracted to a 'onedimensional'
absolute intrinsic metric space denoted by φρ, which is curved onto the
absolute time/absolute intrinsic time 'dimensions' along the vertical and that the underlying
projective three-dimensional flat proper intrinsic metric space φE'^{3} is perfectly
isotropic and is consequently contracted to a straight line one-dimensional isotropic
proper intrinsic metric space φρ' along the horizontal, with respect to observers in the
physical proper Euclidean 3-space φE'^{3} that overlies φρ', are deduced.

**Comments:** 20 pages. Submitted to Progress in Physics

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[v1] 30 Nov 2010

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