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Casimir Elements and Bochner Identities on Riemannian Manifolds

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Clifford Algebras

Part of the book series: Progress in Mathematical Physics ((PMP,volume 34))

Abstract

We show that the principal symbols of first order geometric differential operators on Riemannian manifolds are controlled by the enveloping algebra and higher Casimir elements of so(n). Then we give all the Bochner identities for the operators explicitly.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo, Japan, 169-8555

    Yasushi Homma

Authors
  1. Yasushi Homma
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Tennessee Technological University, 5054, TN 38505, Cookeville, USA

    Rafał Abłamowicz

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© 2004 Birkhäuser Boston

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Homma, Y. (2004). Casimir Elements and Bochner Identities on Riemannian Manifolds. In: Abłamowicz, R. (eds) Clifford Algebras. Progress in Mathematical Physics, vol 34. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2044-2_12

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  • DOI: https://doi.org/10.1007/978-1-4612-2044-2_12

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3525-1

  • Online ISBN: 978-1-4612-2044-2

  • eBook Packages: Springer Book Archive

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