Mokhov, O. I. Flat pencils of metrics and integrable reductions of Lamé’s equations. (English. Russian original) Zbl 1006.53017 Russ. Math. Surv. 56, No. 2, 416-418 (2001); translation from Usp. Mat. Nauk 56, No. 2, 221-222 (2001). The author proposes a method of solving a particular system of PDE’s which is obtained by reduction of so called Lamé equations related to the problem of compatibility of flat pseudo-Riemannian metrics. (Two such metrics \(g_1\) and \(g_2\) are said to be compatible iff the Levi-Civita connections and curvature tensors of any linear combination \(a_1g_1 + a_2g_2\) with constant coefficients \(a_i\) are of the form \(a_1\nabla_1 + a_2\nabla_2\) and \(a_1R_1 + a_2R_2\), \(\nabla_i\) and \(R_i\) being the Levi-Civita connections and curvature tensors of \(g_i\), \(i = 1, 2\)). Reviewer: Pawel Walczak (Łódź) Cited in 4 Documents MSC: 53B21 Methods of local Riemannian geometry Keywords:pseudo-Riemannian metrics; compatibility; pencil; Lamé equations PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 56, No. 2, 416--418 (2001; Zbl 1006.53017); translation from Usp. Mat. Nauk 56, No. 2, 221--222 (2001) Full Text: DOI