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

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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, Number 10, Pages 54–61 (Mi ivm8941)

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

Theorems of existence and non-existence of conformal Killing forms

S. E. Stepanov^a, I. I. Tsyganok^b

^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

Full-text PDF (195 kB) Citations (10)

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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

$p=1,2,\dots,n-1$ . 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.

Received: 30.03.2013

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2014, Volume 58, Issue 10, Pages 46–51
DOI: https://doi.org/10.3103/S1066369X14100077

Bibliographic databases:

Document Type: Article

UDC: 514.764

Language: Russian

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

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\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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84906854845}

Linking options:

https://www.mathnet.ru/eng/ivm8941

https://www.mathnet.ru/eng/ivm/y2014/i10/p54

This publication is cited in the following 10 articles:

Mikes J., Rovenski V., Stepanov S., Tsyganok I., “Application of the Generalized Bochner Technique to the Study of Conformally Flat Riemannian Manifolds”, Mathematics, 9:9 (2021), 927
Rovenski V., Stepanov S., Tsyganok I., “The Sampson Laplacian on Negatively Pinched Riemannian Manifolds”, Int. Electron. J. Geom., 14:1 (2021), 91–99
Mikes J., Rovenski V., Stepanov S.E., “An Example of Lichnerowicz-Type Laplacian”, Ann. Glob. Anal. Geom., 58:1 (2020), 19–34
S. E. Stepanov, I. I. Tsyganok, “On the Tachibana numbers of closed manifolds with pinched negative sectional curvature”, Differ. Geom. Mnogoobr. Figur, 2020, no. 51, 116
V. Rovenski, S. Stepanov, I. Tsyganok, “On the Betti and Tachibana numbers of compact Einstein manifolds”, Mathematics, 7:12 (2019), 1210
I. G. Shandra, S. E. Stepanov, J. Mikes, “On higher-order codazzi tensors on complete Riemannian manifolds”, Ann. Glob. Anal. Geom., 56:3 (2019), 429–442
N. O. Vesic, “Generalized Weyl conformal curvature tensor of generalized Riemannian space”, Miskolc Math. Notes, 20:1 (2019), 555–563
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
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
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Известия высших учебных заведений. Математика

Russian Mathematics (Izvestiya VUZ. Matematika)

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