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Curvature and tachibana numbers

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Abstract

The purpose of this paper is to define the rth Tachibana number t r of an n-dimensional closed and oriented Riemannian manifold (M,g) as the dimension of the space of all conformal Killing r-forms for r = 1, 2, . . . , n − 1 and to formulate some properties of these numbers as an analog of properties of the rth Betti number b r of a closed and oriented Riemannian manifold.

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Authors and Affiliations

  1. Department of Mathematics, Financial Academy under the Government of the Russian Federation, 125468, Moscow, Russia

    S. E. Stepanov

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  1. S. E. Stepanov
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Correspondence to S. E. Stepanov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 6, pp. 211–222, 2009.

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Stepanov, S.E. Curvature and tachibana numbers. J Math Sci 172, 901–908 (2011). https://doi.org/10.1007/s10958-011-0232-y

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  • DOI: https://doi.org/10.1007/s10958-011-0232-y

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