Keywords
principal cycle
curvature lines. MSC
53C12
34D30
53A05
37C75
curvature lines. MSC
53C12
34D30
53A05
37C75
How to Cite
Curvature lines on orthogonal surfaces of R3 and Joachimsthal Theorem. (2005). Civilizar, 5(8), 63-76. https://doi.org/10.22518/16578953.800
Abstract
In this paper is studied, as a complement of Joachimsthal theorem, the behavior of curvature lines near a principal cycle common to two orthogonal surfaces.References
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C. Gutierrez and J. Sotomayor, Closed principal lines and bifurcation, Bull. Braz.
Math. Soc. 17, 1986, pp. 1-19
R. Garcia and J. Sotomayor Lectures Notes on Qualitative Theory of Differential
Equations of Classical Geometry , Notas de Curso, IME/UFG, (2000).
A. Gray, L. Cordeiro and M. Fernandez ´ , Geometr´ıa diferencial de curvas y superficies,
con Mathematica, Addison-Wesley Iberoamericana, (1995).
C. Gutierrez and J. Sotomayor, Lines of Curvature and Umbilic Points on Surfaces,
Brazilian 18th Math. Coll., IMPA, 1991, Reprinted as Structurally Configurations of
Lines of Curvature and Umbilic Points on Surfaces, Monografias del IMCA, (1998).
H. Hopf, Differential Geometry in the Large, Springer Lecture Notes in Mathematics,
vol. 1000, (1983).
D. Hilbert and S. Cohn Vossen Geometry and the Imagination, Chelsea, (1952).
G. Monge Journ. de l’Ecole Polytech, IIe, (1796), Applications de l’Algebre a la
Geometrie, Paris, (1850).
M. Spivak A Comprehensive Introduction to Differential Geometry, vol.III, V, Publish
of Perish Berkeley, (1979).
D. Struik Lectures on Classical Differential Geometry, Addison Wesley, (1950),
Reprinted by Dover Collections, (1978).
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