### Abstract

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 ∧^{2}V 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 language | English (US) |
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Pages (from-to) | 93-105 |

Number of pages | 13 |

Journal | Linear and Multilinear Algebra |

Volume | 7 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1979 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory