Ruled Surfaces as Pseudospherical Congruences

  • V. O. Gorkavyy B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv, 61103, Ukraine
  • O. M. Nevmerzhitska B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv, 61103, Ukraine

Анотація

Two-dimensional ruled surfaces in the spaces of constant curvature Rn, Sn, Hn and in the Riemannian products Sn × R1, Hn × R1 are considered. A ruled surface is proved to represent a pseudospherical congruence if and only if it is either an intrinsically flat surface in Sn, or an intrinsically flat surface with constant extrinsic curvature in Sn × R1.

Mathematics Subject Classification: 53B25, 53A07.

Ключові слова:

pseudo-spherical congruence, ruled surface

Downloads

Як цитувати

(1)
V. O. Gorkavyy і O. M. Nevmerzhitska, Ruled Surfaces as Pseudospherical Congruences, Журн. мат. фіз. анал. геом. 5 (2009), 359-374.

Номер

Том 5 № 4 (2009)

Розділ

Статті

Завантаження

Дані завантаження ще не доступні.