The Kernel of the Rarita–Schwinger Operator on Riemannian Spin Manifolds

Yasushi Homma, Uwe Semmelmann

    Research output: Contribution to journalArticle

    Abstract

    We study the Rarita–Schwinger operator on compact Riemannian spin manifolds. In particular, we find examples of compact Einstein manifolds with positive scalar curvature where the Rarita–Schwinger operator has a non-trivial kernel. For positive quaternion Kähler manifolds and symmetric spaces with spin structure we give a complete classification of manifolds admitting Rarita–Schwinger fields. In the case of Calabi–Yau, hyperkähler, G2 and Spin(7) manifolds we find an identification of the kernel of the Rarita–Schwinger operator with certain spaces of harmonic forms. We also give a classification of compact irreducible spin manifolds admitting parallel Rarita–Schwinger fields.

    Original languageEnglish
    JournalCommunications in Mathematical Physics
    DOIs
    Publication statusPublished - 2019 Jan 1

    Fingerprint

    kernel
    operators
    Operator
    Harmonic Forms
    Positive Scalar Curvature
    Spin Structure
    Einstein Manifold
    Quaternion
    quaternions
    Symmetric Spaces
    Compact Manifold
    curvature
    scalars
    harmonics

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

    The Kernel of the Rarita–Schwinger Operator on Riemannian Spin Manifolds. / Homma, Yasushi; Semmelmann, Uwe.

    In: Communications in Mathematical Physics, 01.01.2019.

    Research output: Contribution to journalArticle

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