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On some families of linear connections. (English) Zbl 1225.53015

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
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