Local Isometry from Complete Manifold is a Covering Map Riemannian Geometry No Ricci-flat Metric on Sphere Times R in Low Dimensions Riemannian Geometry Pullback Metric via Immersion Riemannian Geometry Restricted Holonomy Lies in SO(n) Riemannian Geometry Hodge Star on Basis Elements Riemannian Geometry Yang-Mills Energy Bound Differential Geometry Involutivity Criterion Differential Geometry Standard Form Theorem Differential Geometry