Riemanian Manifolds of Asymmetric Equilibria: Complete Geometric Structure and Curvature Signatures

We develop the complete Riemannian geometry of Victoria–Nash asymmetric equilibrium manifolds (VNAE) for $n$-player games. The metric \(g_{ij} = \iota_i \iota_j \delta_{ij} + \varepsilon H_{ij}(V,\iota)\) yields explicit Levi-Civita connection \(\Gamma^k_{ij}\), Riemann tensor \(R^i_{\,jkl}\) with fourth-order $V$-derivative cancellation, Ricci tensor \(R_{ij} \approx \kappa\bigl(\iota_{i,j} \iota_i - \kappa \partial_i^2 \iota_i\bigr) \delta_{ij}\), and scalar curvature \(K_s \approx \sum_{i