Brief communications

Three classes of Weitzenböck manifolds

I. A. Gordeeva^a, S. E. Stepanov<sup>b

a</sup> Chair of Information Science, Vladimir State University, Vladimir, Russia
^b Chair of Mathematics, Financial University at the Government of the Russian Federation, Moscow, Russia

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.

UDC: 514.764+514.822

Presented by the member of Editorial Board: V. V. Shurygin
Received: 17.03.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:1, 83–85

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