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Mat. Zametki, 2006, Volume 80, Issue 6, Pages 902–907 (Mi mz3365)  

This article is cited in 10 scientific papers (total in 10 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.

DOI: https://doi.org/10.4213/mzm3365

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English version:
Mathematical Notes, 2006, 80:6, 848–852

Bibliographic databases:

UDC: 514.764.212
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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. E. Stepanov, “Curvature and Tachibana numbers”, J. Math. Sci., 172:6 (2011), 901–908  mathnet  crossref  mathscinet
    2. S. E. Stepanov, “Curvature and Tachibana numbers”, Sb. Math., 202:7 (2011), 1059–1069  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Stepanov S.E. Mikes J., “Betti and Tachibana Numbers of Compact Riemannian Manifolds”, Differ. Geom. Appl., 31:4 (2013), 486–495  crossref  mathscinet  zmath  isi  elib  scopus
    4. Stepanov S.E. Mikes J., “Betti and Tachibana Numbers”, Miskolc Math. Notes, 14:2 (2013), 475–486  mathscinet  zmath  isi
    5. S. E. Stepanov, “Betti and Tachibana Numbers”, Math. Notes, 95:6 (2014), 856–864  mathnet  crossref  crossref  mathscinet  isi  elib
    6. S. E. Stepanov, I. I. Tsyganok, “Theorems of existence and non-existence of conformal Killing forms”, Russian Math. (Iz. VUZ), 58:10 (2014), 46–51  mathnet  crossref
    7. Stepanov S.E., Jukl M., Mikes J., “On Dimensions of Vector Spaces of Conformal Killing Forms”, Algebra, Geometry and Mathematical Physics, Springer Proceedings in Mathematics & Statistics, 85, eds. Makhlouf A., Paal E., Silvestrov S., Stolin A., Springer, 2014, 495–507  crossref  mathscinet  zmath  isi  scopus
    8. Stepanov S.E., Mikes J., “Eigenvalues of the Tachibana Operator Which Acts on Differential Forms”, Differ. Geom. Appl., 35:1 (2014), 19–25  crossref  mathscinet  zmath  isi  scopus
    9. S. E. Stepanov, J. Mikeš, “The Hodge–de Rham Laplacian and Tachibana operator on a compact Riemannian manifold with curvature operator of definite sign”, Izv. Math., 79:2 (2015), 375–387  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. Stepanov S.E., Tsyganok I.I., Mikes J., “Overview and Comparative Analysis of the Properties of the Hodge-de Rham and Tachibana Operators”, Filomat, 29:10 (2015), 2429–2436  crossref  mathscinet  zmath  isi  scopus
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