Resumen
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.Citas
M. Berger and B. Gostiaux Introduction to Differential Geometry, Springer Verlag,
New York, (1987).
M. do Carmo, Differential Geometry of curves and surfaces, Prentice Hall, New Jersey,
(1976).
G. Darboux Le¸cons sur la Th´eorie des Surfaces, vol.I, IV, Gauthiers Villars, (1896).
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).
New York, (1987).
M. do Carmo, Differential Geometry of curves and surfaces, Prentice Hall, New Jersey,
(1976).
G. Darboux Le¸cons sur la Th´eorie des Surfaces, vol.I, IV, Gauthiers Villars, (1896).
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).
Una vez publicado, los derechos de impresión y reproducción son del Universidad Sergio Arboleda. Es potestativo del editor permitir la reproducción del artículo.
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