Properties of the exterior algebra of a vector space are used to investigate the curvature operator of a Riemannian manifold. Induced inner products and linear maps are used to establish results about the Euler characteristic of a compact manifold. An open problem about the decomposition of operators on ∧2V is discussed. This problem arises in the study of the codimension needed for isometric embeddings. A new algebraic consequence of the first Bianchi identities is established.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory