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Conformal Killing forms on Riemannian manifolds

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Abstract

Conformal Killing forms are a natural generalization of conformal vector fields on Riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We show the existence of conformal Killing forms on nearly Kähler and weak G 2 -manifolds. Moreover, we give a complete description of special conformal Killing forms. A further result is a sharp upper bound on the dimension of the space of conformal Killing forms.

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Authors and Affiliations

  1. Mathematische Institut, Ludwig-Maximillians-Universität München, 80333, München, Germany

    Uwe Semmelmann

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  1. Uwe Semmelmann
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The author is a member of the European Differential Geometry Endeavour (EDGE), Research Training Network HPRN-CT-2000-00101, supported by The European Human Potential Programme.

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Semmelmann, U. Conformal Killing forms on Riemannian manifolds. Math. Z. 245, 503–527 (2003). https://doi.org/10.1007/s00209-003-0549-4

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  • DOI: https://doi.org/10.1007/s00209-003-0549-4

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