Some Cohomology Classes in Principal Fiber Bundles and Their Application to Riemannian Geometry

Abstract

We define some new global invariants of a fiber bundle with a connection. They are cohomology classes in the principal fiber bundle that are defined when certain characteristic curvature forms vanish. In the case of the principal tangent bundle of a riemannian manifold, they are invariant under a conformal transformation of the metric. They give necessary conditions for conformal immersion of a riemannian manifold in euclidean space.