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Sbornik: Mathematics, 2011, Volume 202, Issue 7, Pages 1059–1069
DOI: https://doi.org/10.1070/SM2011v202n07ABEH004177 (Mi sm7711) 		 
This article is cited in 19 scientific papers (total in 19 papers)

Curvature and Tachibana numbers

S. E. Stepanov

Finance Academy under the Government of the Russian Federation
English version PDF (442 kB) Citations (19)
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DOI: https://doi.org/10.1070/SM2011v202n07ABEH004177
Abstract: The aim of this paper is to define the $r$th Tachibana number $t_r$ of an $n$-dimensional compact oriented Riemannian manifold as the dimension of the space of conformally Killing $r$-forms, for $r=1,2,\dots,n-1$. We also describe properties of these numbers, by analogy with properties of the Betti numbers $b_r$ of a compact oriented Riemannian manifold.
Bibliography: 25 titles.
Keywords: compact Riemannian manifold, differential forms, elliptic operator, scalar invariants.
Received: 13.03.2010 and 12.12.2010
Russian version:
Matematicheskii Sbornik, 2011, Volume 202, Number 7, Pages 135–146
DOI: https://doi.org/10.4213/sm7711
Bibliographic databases:
Document Type: Article
UDC: 514.762.212
MSC: 53C21, 58A10
Language: English
Original paper language: Russian
Citation: S. E. Stepanov, “Curvature and Tachibana numbers”, Mat. Sb., 202:7 (2011), 135–146; Sb. Math., 202:7 (2011), 1059–1069
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v202/i7/p135
    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:626
    Russian version PDF:210
    English version PDF:11
    References:90
    First page:54
     
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