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Theorems of existence and of vanishing of conformally killing forms

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Abstract

On an n-dimensional compact, orientable, connected Riemannian manifold, we consider the curvature operator acting on the space of covariant traceless symmetric 2-tensors. We prove that, if the curvature operator is negative, then the manifold admits no nonzero conformally Killing p-forms for p = 1, 2, …, n − 1. On the other hand, we prove that the dimension of the vector space of conformally Killing p-forms on an n-dimensional compact simply-connected conformally flat Riemannian manifold (M,g) is not zero.

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Authors and Affiliations

  1. Financial University at the Government of the Russian Federation, Leningradskii pr., 49-55, Moscow, 125993, Russia

    S. E. Stepanov & I. I. Tsyganok

Authors
  1. S. E. Stepanov
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  2. I. I. Tsyganok
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Correspondence to S. E. Stepanov.

Additional information

Original Russian Text © S.E. Stepanov, I.I. Tsyganok, 2014, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 10, pp. 54–61.

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Stepanov, S.E., Tsyganok, I.I. Theorems of existence and of vanishing of conformally killing forms. Russ Math. 58, 46–51 (2014). https://doi.org/10.3103/S1066369X14100077

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  • DOI: https://doi.org/10.3103/S1066369X14100077

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