Curvature Operators on the Exterior Algebra

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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.

Original languageEnglish (US)
Pages (from-to)93-105
Number of pages13
JournalLinear and Multilinear Algebra
Issue number2
StatePublished - Jan 1 1979


All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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