Abstract
In this paper on the simplest examples of compact 4-dimensional conformally connected manifolds (real quadrics in a 5-dimensional projective space) we show that the only invariant, which is quadratic with respect to the curvature Φ of the connectivity, is the Yang-Mills functional ε |tr (*Φ Λ Φ)|. We do not know whether the 4-form |tr (*Φ Λ Φ)| is invariant in any 4-dimensional conformally connected manifolds.
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References
A. L. Besse, Einstein Manifolds (Springer, Berlin, 1987; Mir, Moscow, 1990), Vol. I.
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Original Russian Text © V.A. Luk’yanov, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 3, pp. 67–72.
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Luk’yanov, A.V. Yang-mills equations in 4-dimensional conformally connected manifolds. Russ Math. 53, 56–60 (2009). https://doi.org/10.3103/S1066369X09030049
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DOI: https://doi.org/10.3103/S1066369X09030049