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On the geometry of the (2n+1)-webs in 2n-dimensional affinely connected spaces A2n

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Abstract

An approach for the investigation of the geometry of (2n+1) -webs in 2n-dimensional affinely connected spaces A2n by means of the prolonged differentiation is given in [1] Using this approach in the present paper some properties of (2n+1)-webs in A2n are studied. Necessary and sufficient conditions under which the generalized affinor of Hess of a (2n+1)-web is covariantly constant are found. The space A2n, containing a (2n+1)-web with a constant covariant generalized affinor of Hess, is determined. Conditions for geodesicity of the lines of a given (2n+1)-web in A2n in terms of its tensor are found, also.

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References

  1. Zlatanov, G.: Geometry of Nets and Webs nin 2n-dimensional Affinely Connected Space. C.R.Acad.Sci.Bulgare, Vol.41, No.9 (1988), 31–34. (In Russian)

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Authors and Affiliations

  1. University of Plovdiv “Paissii Hilendarski”, 24 Tsar Assen Str., 4000, Plovdiv, Bulgaria

    Georgy Zlatanov

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  1. Georgy Zlatanov
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The present investigation is partially supported by the Ministry of Science and Higher Education of People's Republic of Bulgaria under grant 1021.

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Zlatanov, G. On the geometry of the (2n+1)-webs in 2n-dimensional affinely connected spaces A2n . J Geom 39, 192–200 (1990). https://doi.org/10.1007/BF01222150

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  • DOI: https://doi.org/10.1007/BF01222150

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