Ruled Surfaces as Pseudospherical Congruences

Автор(и)

  • 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

Ключові слова:

pseudo-spherical congruence, ruled surface

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.

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Як цитувати

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

Номер

Том 5 № 4 (2009)

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