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

Yasushi Homma, Uwe Semmelmann

    研究成果: Article

    抄録

    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.

    元の言語English
    ジャーナルCommunications in Mathematical Physics
    DOI
    出版物ステータスPublished - 2019 1 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

    これを引用

    @article{b10c3d73bc7147bf9163df5228e7dbb7,
    title = "The Kernel of the Rarita–Schwinger Operator on Riemannian Spin Manifolds",
    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 K{\"a}hler manifolds and symmetric spaces with spin structure we give a complete classification of manifolds admitting Rarita–Schwinger fields. In the case of Calabi–Yau, hyperk{\"a}hler, 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.",
    author = "Yasushi Homma and Uwe Semmelmann",
    year = "2019",
    month = "1",
    day = "1",
    doi = "10.1007/s00220-019-03324-8",
    language = "English",
    journal = "Communications in Mathematical Physics",
    issn = "0010-3616",
    publisher = "Springer New York",

    }

    TY - JOUR

    T1 - The Kernel of the Rarita–Schwinger Operator on Riemannian Spin Manifolds

    AU - Homma, Yasushi

    AU - Semmelmann, Uwe

    PY - 2019/1/1

    Y1 - 2019/1/1

    N2 - 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.

    AB - 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.

    UR - http://www.scopus.com/inward/record.url?scp=85061087715&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85061087715&partnerID=8YFLogxK

    U2 - 10.1007/s00220-019-03324-8

    DO - 10.1007/s00220-019-03324-8

    M3 - Article

    AN - SCOPUS:85061087715

    JO - Communications in Mathematical Physics

    JF - Communications in Mathematical Physics

    SN - 0010-3616

    ER -