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Kählerian twistor spinors

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Abstract

On a Kähler spin manifold, Kählerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the Kähler structure, called Kählerian twistor (Penrose) operator. We study Kählerian twistor spinors and give a complete description of compact Kähler manifolds of constant scalar curvature admitting such spinors. As in the Riemannian case, the existence of Kählerian twistor spinors is related to the lower bound of the spectrum of the Dirac operator.

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Authors and Affiliations

  1. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931, Cologne, Germany

    Mihaela Pilca

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  1. Mihaela Pilca
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Correspondence to Mihaela Pilca.

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The author thanks Graduiertenkolleg 1269 “Global Structures in Geometry and Analysis” for financial support and the Centre de Mathématiques “Laurent Schwartz” de l’École Polytechnique for hospitality during part of the preparation of this work, within the French–German cooperation project Procope no. 17825PG.

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Pilca, M. Kählerian twistor spinors. Math. Z. 268, 223–255 (2011). https://doi.org/10.1007/s00209-010-0668-7

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  • DOI: https://doi.org/10.1007/s00209-010-0668-7

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