Two-dimensional ruled surfaces in the spaces of constant curvature Rⁿ, Sⁿ, Hn and in the Riemannian products Sⁿ x R¹, Hⁿ x 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 x R¹.
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机译:在等曲率R 1,S 4,H n的空间和黎曼积S 1 x R 1,H 4 x R 1的空间中考虑了二维直纹表面。当且仅当规则面是Sⁿ中的本征平面或Sⁿx R 1中具有恒定外在曲率的本征平面时,方可证明该伪面为伪球面同余。
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