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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 3, Pages 82–92 (Mi ivm9095)  
This article is cited in 1 scientific paper (total in 1 paper)

Bol three-webs with covariant constant curvature tensor

A. M. Shelekhova, E. A. Onoprienkob

a Chair of Functional Analysis and Geometry, Tver State University, 33 Zhelyabova str., Tver, 170100 Russia
b Chair of Geometry, Moscow Pedagogical State University, 1 M. Pirogovskaya str., Moscow, 119991 Russia
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Abstract: We find complete system of tensor relations characterizing the class of multidimensional middle Bol three-webs with covariant constant curvature tensor and ascertain the algebraic sense of these relations. We prove the existence of such webs and lay the foundation of their classification in terms of torsion tensor rank. We show that $6$-dimensional non-group webs of such type are the known flexible webs $E_1$ and $E_2$.
Keywords: three-web, middle Bol three-web, flexible three-web, $W$-algebra, Chern connection of a three-web, commutator, associator, holonomy algebra.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1686
Received: 18.08.2014
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 3, Pages 72–81
DOI: https://doi.org/10.3103/S1066369X16030099
Bibliographic databases:
Document Type: Article
UDC: 514.763
Language: Russian
Citation: A. M. Shelekhov, E. A. Onoprienko, “Bol three-webs with covariant constant curvature tensor”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 3, 82–92; Russian Math. (Iz. VUZ), 60:3 (2016), 72–81
Citation in format AMSBIB
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\pages 82--92
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\issue 3
\pages 72--81
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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