Geometrical Description Of Monkey’s Saddle

  • Miloš Kaňka Department of Mathematics and Statistics, College of Polytechnics Jihlava
  • Eva Kaňková Faculty of Business Administration, University of Economics, Prague
Keywords: , Cartan’s Moving Frame Method, Weingarten Map, Gaussian Curvature, Main Curvature, Moving Frame

Abstract

The principal object of this paper is the regular parametric surface M in  defined by the formula . The geometrical description methods we are going to use are based on Cartan’s moving frame method and on Weingarten map. The studied map  is  regular

References

Bochner, S. “A new viewpoint in differential geometry.” Canadian Journal of mathematics – Journal Canadian de Mathematiques. 1951: 460–470.

Bureš, J., Kaňka, M. “Some Conditions for a Surface in E4 to be a Part of the Sphere S2”. Mathematica Bohemica 4 1994. s. 367–371.

Cartan, É. Oeuvres complètes-Partie I Vol. 2. Paris: Gauthier-Villars, 1952.

Cartan, É. Oeuvres complètes-Partie II Vol. 1. Paris: Gauthier-Villars, 1953.

Cartan, É. Oeuvres complètes-Partie II Vol. 2. Paris: Gauthier-Villars, 1953.

Cartan, É. Oeuvres complètes-Partie III Vol. 1. Paris: Gauthier-Villars, 1955.

Cartan, É. Oeuvres complètes-Partie III Vol. 2. Paris: Gauthier-Villars, 1955.

Kaňka, M. “Example of Basic Structure Equations of Riemannian Manifolds”, Mundus Symbolicus 3 1995. s. 57–62.

Chern, SS. “Some new Viewpoints in Differential geometry in the large.” Bulletin of the American mathematical Society. 1946: 1–30.

Kobayashi, S., Nomizu, K. Foundations of Differential Geometry. New York: Wiley (Inter-science), 1963.

Kostant, B. “On differential geometry and homogeneous space. 1.” Proceedings of the national Academy of sciences of the United States of America. 1956: 258–261.

Kostant, B. “On differential geometry and homogeneous space. 2.” Proceedings of the national Academy of sciences of the United States of America. 1956: 354–357.

Nomizu, K. Lie Groups and Differential Geometry. Tokyo: The Mathematical Society of Japan, 1956.

Rauch, H. “A contribution to differential geometry in the large.” Annals of Mathematics. 1961:38–55.

Sternberg, S. Lectures on Differential Geometry. Englewood Cliffs, N.J.: Prentice-Hall, 1964.

Published
2012-09-01
Section
Articles