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This article is cited in 15 scientific papers (total in 15 papers)
Some conformal and projective scalar invariants of Riemannian manifolds
S. E. Stepanov Vladimir State Pedagogical University
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 $1\le r\le n-1$,
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.
Received: 26.09.2005 Revised: 03.05.2006
Citation:
S. E. Stepanov, “Some conformal and projective scalar invariants of Riemannian manifolds”, Mat. Zametki, 80:6 (2006), 902–907; Math. Notes, 80:6 (2006), 848–852
Linking options:
https://www.mathnet.ru/eng/mzm3365https://doi.org/10.4213/mzm3365 https://www.mathnet.ru/eng/mzm/v80/i6/p902
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