The kernel of the rarita-schwinger operator on riemannian spin manifolds


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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.

MSC Codes 32Q20, 57R20, 53C26, 53C27 53C35, 53C15

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2018 Apr 27


  • Dirac operator
  • Manifolds of special holonomy
  • Rarita-Schwinger operator,Weitzenböck formulas
  • Spin manifolds

ASJC Scopus subject areas

  • General

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