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Izv. Vyssh. Uchebn. Zaved. Mat., 2014, Number 10, Pages 54–61 (Mi ivm8941)  

This article is cited in 3 scientific papers (total in 3 papers)

Theorems of existence and non-existence of conformal Killing forms

S. E. Stepanova, I. I. Tsyganokb

a Chair of Mathematics, Financial University at the Government of the Russian Federation, 49–55 Leningradskii Ave., Moscow, 125993 Russia
b Chair of Probability theory and Mathematical Statistics, Financial University at the Government of the Russian Federation, 49–55 Leningradskii Ave., Moscow, 125993 Russia

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, the manifold admits no nonzero conformal Killing $p$-forms for $p=1,2,…,n-1$. On the other hand, we prove that the dimension of the vector space of conformal Killing $p$-forms on an $n$-dimensional compact simply-connected conformally flat Riemannian manifold $(M, g)$ is not zero.

Keywords: Riemannian manifold, curvature operator, conformal Killing forms, vanishing theorem, existence theorem.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, 58:10, 46–51

UDC: 514.764
Received: 30.03.2013

Citation: S. E. Stepanov, I. I. Tsyganok, “Theorems of existence and non-existence of conformal Killing forms”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, no. 10, 54–61; Russian Math. (Iz. VUZ), 58:10 (2014), 46–51

Citation in format AMSBIB
\Bibitem{SteTsy14}
\by S.~E.~Stepanov, I.~I.~Tsyganok
\paper Theorems of existence and non-existence of conformal Killing forms
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2014
\issue 10
\pages 54--61
\mathnet{http://mi.mathnet.ru/ivm8941}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2014
\vol 58
\issue 10
\pages 46--51
\crossref{https://doi.org/10.3103/S1066369X14100077}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84906854845}


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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, 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
    2. 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  isi  elib
    3. S. Stepanov, I. Tsyganok, “Conformal Killing $L^2$-forms on complete Riemannian manifolds with nonpositive curvature operator”, J. Math. Anal. Appl., 458:1 (2018), 1–8  crossref  mathscinet  zmath  isi  scopus
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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