Specially defined Calabi-Yau manifolds having the hypersurfaces of degree - 5 in ℙ⁴ satisfying the non-trivial canonical bundle Λˣ₃ where the embedding holomorphic map ψ∶ X⟶ ℙ with the Kähler form for holomorphic line bundle giving a strictly positive parameter ℓᵏ ⨂ ∃k > 0 representing ℓ through the first Chern Class H² (2,ℤ). When for every Kähler Class , the Cohomology class exists with the compact form (X,ω) ∀ potential spaces satisfying H²ₔᵣ (X) with the ∂∂*−lemma for a harmonic form giving us the (1,1)⁺ − Kähler potential 𝒊2⁻¹∂∂*ρ. Taking all this in effect and making it established through various conjectures, axioms, ideals, theorems – an equivalence class is shown between the structures: Kahler-Manifold, Calabi-Yau-Manifold, Hyperkahler-Manifold, Quintic-3-Fold, Kummer Surface, K–3 Surface, De Rahm Cohomology Class (Hol(Ω(μ,ν)). The extreme case considered here is the exclusion of Complex hyperbolic Kahler – represented by ℂℙⁿ ∀n = -1. In course of making this paper the non–trivial aspects concerning the topological structures in aspects of string theory, the compact Kahler with a Ricci–flatness explained here.