Abstract
In this paper we extend the Darboux theory of integrability in ℝ n to the regular algebraic hypersurfaces. Then we apply the extended theory first to the 3-dimensional generalized cylinders (S 1) × ℝ 3-r of ℝ 4 for r=0, 1, 2, 3; and after to then-dimensional sphere S n of ℝ n+1. © 2002 Springer.
Original language | English |
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Pages (from-to) | 109-126 |
Journal | Rendiconti del Circolo Matematico di Palermo |
Volume | 51 |
DOIs | |
Publication status | Published - 1 Feb 2002 |
Keywords
- Darboux integrability
- generalized cylinder
- sphere
- torus