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.
- Publication:
-
Proceedings of the National Academy of Science
- Pub Date:
- April 1971
- DOI:
- 10.1073/pnas.68.4.791
- Bibcode:
- 1971PNAS...68..791C