Twisted Dirac operators and generalized gradients

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    2 Citations (Scopus)

    Abstract

    On Riemannian or spin manifolds, there are geometric first order differential operators called generalized gradients. In this article, we prove that the Dirac operator twisted with an associated bundle is a linear combination of some generalized gradients. This observation allows us to find all the homomorphism type Weitzenböck formulas. We also give some applications.

    Original languageEnglish
    Pages (from-to)1-27
    Number of pages27
    JournalAnnals of Global Analysis and Geometry
    DOIs
    Publication statusAccepted/In press - 2016 Mar 3

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    Keywords

    • Dirac operator
    • Generalized gradient
    • Lichnerowicz Laplacian
    • Weitzenböck formulas

    ASJC Scopus subject areas

    • Geometry and Topology
    • Analysis
    • Political Science and International Relations

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