Об изменении кривизны конформно-плоской метрики при преобразовании Лежандра

Article Russian OPEN
Куркина, М.В.;
(2018)

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. Br... View more
  • References (7)

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

    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.

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