### 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, G_{2} 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 language | English |
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Journal | Communications in Mathematical Physics |

DOIs | |

Publication status | Published - 2019 Jan 1 |

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### 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.

Research output: Contribution to journal › Article

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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

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -