S. E. Stepanov, “Curvature and Tachibana numbers”, Sb. Math., 202:7 (2011), 1059

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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) Russian version article

References:

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DOI: https://doi.org/10.1070/SM2011v202n07ABEH004177

Abstract: The aim of this paper is to define the

r

$r$ th Tachibana number

t_{r}

$t_r$ of an

n

$n$ -dimensional compact oriented Riemannian manifold as the dimension of the space of conformally Killing

r

$r$ -forms, for

r = 1, 2, \dots, n - 1

$r=1,2,\dots,n-1$ . We also describe properties of these numbers, by analogy with properties of the Betti numbers

b_{r}

$b_r$ 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

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”, Sb. Math., 202:7 (2011), 1059–1069

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sm7711

https://doi.org/10.1070/SM2011v202n07ABEH004177

https://www.mathnet.ru/eng/sm/v202/i7/p135

This publication is cited in the following 19 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
Rovenski V., Stepanov S., Tsyganok I., “On the Betti and Tachibana Numbers of Compact Einstein Manifolds”, Mathematics, 7:12 (2019), 1210
Stepanov S., Tsyganok I., “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, I. I. Tsyganok, T. V. Dmitrieva, “Harmonic and conformally Killing forms on complete Riemannian manifold”, Russian Math. (Iz. VUZ), 61:3 (2017), 44–48
Irina Alexandrova, Irina Alexandrova, Sergey Stepanov, Sergey Stepanov, Irina Tsyganok, Irina Tsyganok, “EXTERIOR DIFFERENTIAL FORMS ON RIEMANNIAN SYMMETRIC SPACES”, Science Evolution, 2017, 49
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
S. E. Stepanov, I. I. Tsyganok, “Comparative Analysis of Spectral Properties of the Hodge–De Rham and Tachibana Operators”, J Math Sci, 207:4 (2015), 614
S. E. Stepanov, I. A. Alexandrova, I. I. Tsyganok, J. Mikeš, “Conformal Killing forms on totally umbilical submanifolds”, Journal of Mathematical Sciences, 217:5 (2016), 525–539
S. E. Stepanov, J. Marek, J. Mikeš, “Vanishing theorems of conformal Killing forms and their applications to electrodynamics in the general relativity theory”, Int. J. Geom. Methods Mod. Phys., 11:9 (2014), 1450039, 8 pp.
S. E. Stepanov, “Betti and Tachibana Numbers”, Math. Notes, 95:6 (2014), 856–864
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
S. E. Stepanov, M. Jukl, J. Mikeš, “On dimensions of vector spaces of conformal killing forms”, Algebra, Geometry and Mathematical Physics, Springer Proceedings in Mathematics & Statistics, 85, Springer, 2014, 495–507
S. E. Stepanov, J. Mikeš, “Eigenvalues of the Tachibana operator which acts on differential forms”, Differential Geom. Appl., 35, suppl. (2014), 19–25
S. E. Stepanov, J. Mikeš, “Betti and Tachibana numbers of compact Riemannian manifolds”, Differential Geom. Appl., 31:4 (2013), 486–495
S. E. Stepanov, J. Mikeš, “Betti and Tachibana numbers”, Miskolc Math. Notes, 14:2 (2013), 475–486
Stepanov S.E., Mikesh I., Tsyganok I.I., “Operator tachibany”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiz.-mat. nauki, 2013, 82–92
S. E. Stepanov, I. Mikesh, I. I. Tsyganok, “Operator Tachibany”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2013, no. 4, 82–92

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

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Abstract page:	690
Russian version PDF:	224
English version PDF:	26
References:	102
First page:	54

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