Abstract
It is proved that, on any closed oriented Riemannian n-manifold, the vector spaces of conformal Killing, Killing, and closed conformal Killing r-forms, where 1 ≤ r ≤ n − 1, have finite dimensions t r , k r , and p r , respectively. The numbers t r are conformal scalar invariants of the manifold, and the numbers k r and p r are projective scalar invariants; they are dual in the sense that t r = t n−r and k r = p n−r . Moreover, an explicit expression for a conformal Killing r-form on a conformally flat Riemannian n-manifold is given.
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Translated from Matematicheskie Zametki, vol. 80, no. 6, 2006, pp. 902–907.
Original Russian Text Copyright © 2006 by S. E. Stepanov.
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Stepanov, S.E. Some conformal and projective scalar invariants of Riemannian manifolds. Math Notes 80, 848–852 (2006). https://doi.org/10.1007/s11006-006-0206-4
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DOI: https://doi.org/10.1007/s11006-006-0206-4