High-dimensional datasets often concentrate near low-dimensional learned manifolds, but optimizing directly on such learned geometric spaces can break the assumptions used in classical Riemannian optimization. This work develops an iso-Riemannian framework with notions of convexity, monotonicity, and Lipschitz continuity induced by an iso-connection rather than the Levi-Civita connection. It introduces iso-Riemannian descent algorithms with convergence guarantees and demonstrates their use for barycenter computation, clustering, and inverse problems on synthetic data and MNIST.