Some cohomology classes in principal fiber bundles and their application to riemannian geometry.
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.
Chern
S S
SS
Department of Mathematics, University of California at Berkeley, Berkeley, Calif. 94720.
Simons
J
J