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On one class of three-webs with partially symmetric curvature tensor

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Abstract

A classification of six-dimensional webs H s by type of the associated Lie algebra is carried out. Two approaches to the investigation of geometry of nontrivial class of webs H s are considered.

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References

  1. M. A. Akivis, “On three-webs of multidimensional surfaces,” Itogi Nauki Tekh. Ser. Probl. Geom. Tr. Geom. Sem., 2, 7–31 (1969).

    MathSciNet  Google Scholar 

  2. M. A. Akivis and A. M. Shelekhov, Geometry and Algebra of Multidimensional Three-Webs, Kluwer Academic, Dordrecht (1992).

    MATH  Google Scholar 

  3. V. P. Botzu, “On isoclinity of four-dimensional hexagonal three-webs,” Deposited at VINITI (1984), No. 5824–84.

  4. S. S. Chern, “Eine Invariantentheorie der Dreigewebe aus r-dimensionalen Mannigfaltigkeiten in R 2r ,” Abh. Math. Sem. Univ. Hamburg, 11, No. 1–2, 333–358 (1936).

    MATH  Google Scholar 

  5. A. M. Shelekhov, “On differential-geometric objects of higher orders of multidimensional three-web,” Itogi Nauki Tekh. Ser. Probl. Geom. Tr. Geom. Sem., 19, 101–154 (1987).

    MathSciNet  Google Scholar 

  6. M. A. Shestakova, “Structure equations of six-dimensional hexagonal three-web,” in: Webs and Quasigroups, KGU, Kalinin (1988), pp. 140–145.

  7. M. A. Shestakova, “An example of hexagonal three-web with partially symmetric curvature tensor,” in: Webs and Quasigroups, KGU, Kalinin (1990), pp. 22–29.

  8. M. A. Shestakova, “On theory of six-dimensional hexagonal three-webs,” in: Webs and Quasigroups, Tver State Univ., Tver (1993), pp. 56–62.

  9. M. A. Shestakova, “Characterization of some hexagonal 3-web in terms of associated Lie algebras,” in: Webs and Quasigroups, Tver State Univ., Tver (1996–1997), pp. 133–141.

  10. M. A. Shestakova, “On geometry of six-dimensional hexagonal three-web \( H_s^1 \),” in: Webs and Quasigroups, Tver State Univ., Tver (2002), pp. 106–117.

  11. I. P. Yegorov, Geometry [in Russian], Prosveshchenie, Moscow (1979).

    Google Scholar 

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Authors and Affiliations

  1. Tver State University, Tver, Russia

    M. A. Shestakova

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  1. M. A. Shestakova
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Correspondence to M. A. Shestakova.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 1, pp. 179–188, 2010.

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Shestakova, M.A. On one class of three-webs with partially symmetric curvature tensor. J Math Sci 177, 638–645 (2011). https://doi.org/10.1007/s10958-011-0490-8

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  • DOI: https://doi.org/10.1007/s10958-011-0490-8

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