Nicolescu, Liviu; Pripoae, Gabriel-Teodor; Damian, Virgil On some families of linear connections. (English) Zbl 1225.53015 Balkan J. Geom. Appl. 16, No. 1, 98-110 (2011). Let \(\hat{g}\) be a conformal class of semi-Riemannian metrics on the manifold \(M\) and \(w\) a Weyl structure on \((M, \hat{g})\) with the corresponding linear connection \(\nabla \). Fix \(g\in \hat{g}\) and its Levi-Civita connection \(\nabla_0\), and consider the family \(\mathcal{C}=\{{\nabla }_{\lambda }:={\nabla }_0+\lambda (\nabla - {\nabla }_0); \lambda \in \mathbb{R}\}\) of linear connections. The present paper is devoted to the study of conditions under which \({\nabla }_{\lambda }\) and \(\nabla \) have (1) the same Ricci tensor, (2) proportional curvature tensors. Reviewer: Radu Miron (Iaşi) MSC: 53B20 Local Riemannian geometry 53B05 Linear and affine connections 53B21 Methods of local Riemannian geometry Keywords:deformation algebra; Weyl structure; Weyl manifold; conformal Weyl connection; families of linear connections PDFBibTeX XMLCite \textit{L. Nicolescu} et al., Balkan J. Geom. Appl. 16, No. 1, 98--110 (2011; Zbl 1225.53015) Full Text: EMIS