On projective spheres and Fubini and Tzitzeica-Wilczyński pseudospheres
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- Proc. Amer. Math. Soc. 93 (1985), 512-520 Request permission
Abstract:
The definition of a projective pseudosphere is given, and the following results are proved: ( 1 ) There exists one and only one Fubini pseudosphere iff \[ L = M = - \frac {{3{\varphi ^2}}}{2},\quad \beta = \gamma = \varphi ;\quad \varphi = \varphi (\tau )\quad (\tau = u + \upsilon ).\] (2) There exist two classes of limiting Tzitzeica- Wilczynski pseudospheres or improper affine spheres. These pseudospheres admit, beside the first directrix or affine normal, the first Fubini principal straight line or the conjugate of the first directrix with respect to the canonical tangent and projective normal. The asymptotes of the pseudosphere are twisted cubics.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 512-520
- MSC: Primary 53A20
- DOI: https://doi.org/10.1090/S0002-9939-1985-0774015-X
- MathSciNet review: 774015