publication . Article . 2018

Об изменении кривизны конформно-плоской метрики при преобразовании Лежандра

Куркина, М.В.;
Open Access Russian
  • Published: 14 Sep 2018 Journal: Izvestiya of Altai State University (issn: 1561-9451, eissn: 1561-9443, Copyright policy)
  • Publisher: Izvestiya of Altai State University
It is known that the theory of conformally flat Riemannian metric is closely associated with pseudo-Euclidean geometry, due to the existence of the canonical isometric embedding conformally flat metric in pseudo-isotropic cone space. This fact was first noticed by H. Brinkmann, and later was used in the works of N. Kuyper. The geometry of homogeneous Riemannian manifolds with a conformally flat Riemannian metric was studied in the papers of A.D. Alekseevsky and B.N. Kimel’feld, in which their classification was given. In the inhomogeneous case such a classification does not exist, therefore, in the study of conformally flat Riemannian manifolds restrictions of v...
arxiv: Mathematics::Differential Geometry

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