Trenčevski, Kostadin On two tensor fields which are analogous to the curvature and torsion tensor fields. (English) Zbl 0885.53014 Mat. Vesn. 49, No. 1, 3-14 (1997). Let \(\xi\) be a vector bundle over a differentiable manifold \(M\). On the bundle \(\xi\) and on the tangent bundle \(TM\) are given connections \(\nabla\) and \(\widetilde{\nabla}\), respectively, and let \(R\), \(\widetilde{R}\) and \(T\) be the curvature tensors of \(\nabla\) and \(\widetilde{\nabla}\) and the torsion of \(\nabla\), respectively. Combining \(\nabla\), \(\widetilde{\nabla}\), \(R\), \(\widetilde{R}\) and \(T\), new tensor fields \(R^*\), \(\widetilde{R}^*\) and \(T^*\) are defined and their basic properties and geometric interpretations are established. The construction of \(R^*\) and \(\widetilde{R}^*\) is motivated by the theory of semi-symmetric manifolds. Bianchi identities for \(R\) and \(\widetilde{R}\) are obtained. All these notions are generalized to the case of a principal \(G\)-bundle in order to study commutativity of its restricted holonomy group under some assumptions. Reviewer: Novica Blažić (Beograd) MSC: 53B05 Linear and affine connections Keywords:curvature; torsion; forms; principal bundle; holonomy group PDFBibTeX XMLCite \textit{K. Trenčevski}, Mat. Vesn. 49, No. 1, 3--14 (1997; Zbl 0885.53014) Full Text: EuDML EMIS