ISSN 0001-4346, Mathematical Notes, 2018, Vol. 103, No. 2, pp. 304–307. © Pleiades Publishing, Ltd., 2018. Original Russian Text © V. E. Berezovskii, I. Hinterleitner, N. I. Guseva, J. Mikeˇ s, 2018, published in Matematicheskie Zametki, 2018, Vol. 103, No. 2, pp. 303–306. SHORT COMMUNICATIONS Conformal Mappings of Riemannian Spaces onto Ricci Symmetric Spaces 1* 2** 3 *** 4 **** V. E. Berezovskii , I. Hinterleitner , N.I.Guseva ,and J. Mikesˇ Uman National University of Horticulture, Ukraine Brno University of Technology, Brno, Czechia Moscow State Pedagogical University, Moscow, Russia Palacky University, Olomouc, Czechia Received July 24, 2017 DOI: 10.1134/S0001434618010315 Keywords: conformal mapping, Riemannian space, Ricci symmetric space. 1. INTRODUCTION Conformal mappings of n-dimensional Riemannian spaces V have been considered by many authors. They ﬁnd applications in general relativity theory (see, e.g., –). In what follows, we assume the signature of the metrics on the spaces V under consideration to be arbitrary; i.e., each V may be a Riemannian space proper or a pseudo-Riemannian space. Brinkmann reduced the question of whether a Riemannian space V , n ≥ 3, can be conformally mapped onto an Einstein space V to the problem of solvability of a nonlinear system of Cauchy-type diﬀerential
Mathematical Notes – Springer Journals
Published: Mar 14, 2018
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