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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, Number 1, Pages 92–95 (Mi ivm8425)  
Brief communications

Three classes of Weitzenböck manifolds

I. A. Gordeevaa, S. E. Stepanovb

a Chair of Information Science, Vladimir State University, Vladimir, Russia
b Chair of Mathematics, Financial University at the Government of the Russian Federation, Moscow, Russia
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Abstract: The Weitzenböck manifold is the triplet defined by a differential manifold with the metric $g$ of a certain signature and linear connection of zero curvature tensor, the nonzero torsion tensor, and the metricity property. The theory of such manifolds is called the “new theory of gravity”. We consider properties of three classes of such manifolds and on this base prove the vanishing thorems.
Keywords: connection with torsion, curvature tensor, torsion tensor, teleparallelism, Weitzenböck spaces.
Presented by the member of Editorial Board: V. V. Shurygin
Received: 17.03.2011
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, Volume 56, Issue 1, Pages 83–85
DOI: https://doi.org/10.3103/S1066369X12010136
Bibliographic databases:
Document Type: Article
UDC: 514.764+514.822
Language: Russian
Citation: I. A. Gordeeva, S. E. Stepanov, “Three classes of Weitzenböck manifolds”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 1, 92–95; Russian Math. (Iz. VUZ), 56:1 (2012), 83–85
Citation in format AMSBIB
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\by I.~A.~Gordeeva, S.~E.~Stepanov
\paper Three classes of Weitzenb\"ock manifolds
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 1
\pages 92--95
\mathnet{http://mi.mathnet.ru/ivm8425}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2975924}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 1
\pages 83--85
\crossref{https://doi.org/10.3103/S1066369X12010136}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862686216}
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