Complete Riemannian metrics ensure that every geodesic in a Riemannian manifold can be extended indefinitely, making the manifold geodesically complete. Their importance lies in their ability to eliminate the pathological behavior of “falling off the edge” and their fundamental role in the global analysis of manifolds. In this paper, we focus on the complete metrics proposed by Gordon. Despite the simplicity of their tensor representation and inverse, most cases lack explicit expressions for the