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
Abstract
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...
Subjects
arxiv: Mathematics::Differential Geometry

1. Brinkmann H.W. On Riemann spaces conformal to Euclidean spaces // Proc. Nat. Acad. Sci. USA 9 (1923), 1-3. [OpenAIRE]

2. Kuiper N.H. On conformally-flat spaces in large // Ann. of Math. (2) 1949. V. 50.

3. Kuiper N.H. On compact conformally Euclidean spaces of dimention >2 // Ann. of Math. (2) 1950. V. 52.

5. Славский В.В. Конформно плоские мет- рики ограниченной кривизны на n-мерной сфере. Исследования по геометрии ˆв целом‰ и матема- тическому анализу. Новосибирск, 1987. Т. 9.

6. Udo Hertrich-Jeromin. Introduction to Mobius Differential Geometry. London mathematical society lecture note series. Cambridge University Press, 2003.

16. Nikonorov Yu.G., Rodionov E.D., Slavskii V.V. Geometry of homogeneoues Riemannian manifolds // Journal of Mathematical Scieces. 2007. V. 146, № 6.

17. Kurkina M.V., Rodionov E.D. and Slavskii V.V. Conformally Convex Functions and Conformally Flat Metrics of Nonnegative Curvature // Doklady Mathematics. 2015. V. 91, № 3.

Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue